There was clearly some history between the two from their time at Aberdeen and while Ferguson was caretaker manager at Scotland.
Sir Alex inherited Strachan when he took over as Manchester United manager. He had been bought from Aberdeen by Ron Atkinson and had already become a fan favourite before Sir Alex arrived.
He had played over 100 games for United by that time and indeed went on to double that number under Ferguson. But he had already joined the regulars in the treatment room in the previous couple of years. Norman Whiteside eventually had to retire early, and Bryan Robson was also often sidelined.
Strachan's four-and-a-half years at United were a time of turmoil and transition. While they won the FA Cup in 1985, they did little else except finish runners-up in the old First Division in 1987/88 between two 11th-place finishes.
But there was bad blood between them, probably starting from their Aberdeen days. Ferguson in his autobiography said of Strachan:
"I decided this man could not be trusted an inch - I would not want to expose my back to him in a hurry,"
We all know you must never cross Sir Alex, as Jaap Stam and Roy Keane found out to their cost.
Luckily there is no remote chance of Tom Cleverley falling out with his manager. Although the young man shows appropriate self-confidence, it is never likely to spill over into arrogance. And he knows his place at Manchester United.
Tom Cleverley's background
There is little comparison between the early years of Cleverley and Strachan except that they were relatively modest. Strachan actually turned down an approach from Manchester United when he was 14 to join Dundee.
Cleverley was born in Hertfordshire but moved to Bradford as a boy, training with Bradford City as a 10-year-old before signing for Manchester United the following year. He is one of the longest serving young players at the club, his first and last choice as a young man.
There were some doubts whether Cleverley would make it due to his diminutive stature, but he showed a fierce determination and his ability was never in doubt.
Luckily he eventually caught up physically and made nine appearances for the Under 18s as a 16-year-old, also getting a game for the reserves.
Unfortunately he had a bad injury setback for seven months, but he became a regular for the reserves in 2007/8, being awarded the captaincy.
His increasingly impressive displays earned him a place on the 2008/9 preseason tour. He was given a squad number as a result and eventually debuted for the first team in 2010/11 in the FA Community Shield where he was a revelation.
In the intervening years he had spent a couple of seasons on loan, first to Leicester City and then a whole season with each of Watford and Wigan. He made a very strong impression with all three clubs but has never shirked his belief that he could become an established player at United.
Unlike Paul Pogba, he was able to see that either through retirement, maturity of players like Scholes or injury he would get his chance.
Fans have never forgotten the impact that he and Anderson had in the terrific comeback at Wembley against Manchester City in 2011. Cleverley was earmarked for a regular starting place, even ahead of the likes of Scholes, but once again injury set him back.
He possibly returned too early from injury and his 2011/12 season was somewhat blighted. So far he has had 19 appearances for United this term and looks to have secured a place in Sir Alex's preferred midfield combination alongside Michael Carrick.
He has already scored some sublime goals, but what makes his partnership with Carrick work is his work-rate, technical skill and ability to link between midfield and attack.
He is not as good a tackler as Strachan, but in the modern game where players fall down far too easily, his harrying of the opposition is one of his best qualities.
Why the new Gordon Strachan?
One of the media's favourite pastimes is to say something like Shinji Kagawa can be the new Paul Scholes.
Nobody can be the new Paul Scholes. Why can't Nick Powell be the new Nick Powell rather than have Sir Alex compare him to Scholes?
There were a few United players we could compare Cleverley to. Indeed, he may well one day be as good as Sir Bobby Charlton.
Sir Bobby played in the days of "inside forwards," and there is no doubt that Cleverley would have thrived in that role, but the English Knight was never much of a defender and you certainly wouldn't describe him as a midfielder. Indeed, Scholes is closer to a comparison with him.
So why not Paul Scholes?
Certainly Cleverley can do many of the things the younger Scholes could do. He was adept at arriving in the box late and scoring goals, whether he was playing at No.10 or in central midfield.
Cleverley can do that, but he is unlikely to be picked at No. 10 in the foreseeable future. Not only that, but while the cross for Robin Van Persie's goal on Sunday showed that Cleverley can hit an exquisite pass, he doesn't quite have Scholes' passing range.
What he does have is a shot in both feet and the ability to arrive late, as he has done a couple of times this season. His goalscoring tally will undoubtedly increase. He has found his confidence and range, and you can see he is technically highly competent at shooting.
In some ways, a better recent comparison would be with Ji Sung Park. His work rate was similar to Cleverley's. He could put a foot in where needed and was an underrated goalscorer as his stats for South Korea show. Park hardly ever let Sir Alex down, and neither will Cleverley.
So we come back to Gordon Strachan.
Strachan was a box-to-box player with a terrific engine when he was fit. In fact he went on to play into his 40s so his time at United was unfortunate in some respects. He left to join Leeds United where he became a further irritant to Sir Alex as they pipped them to the title in 1991/2.
He was Leeds' driving force, scoring several goals, some of which are not unlike Cleverley.
Strachan was diminutive, rather like his predecessors Johnny Giles and Billy Bremner, at 5'5". While Cleverley is four inches taller, he is not as "chunky" as Strachan was.
The only significant playing difference was that Strachan was the better tackler, but again it must be said that you could get away with far more in those days. Cleverley has had to throttle back in that respect with less tolerance from referees.
But United's No. 23 certainly has the engine to play from box to box as his performances against Liverpool and Tottenham have shown.
He is good on the ball, links up well anywhere from midfield through to the penalty area and pops up to score important goals.
If he stays fit he could well go on to be a mainstay of United for many years to come and comfortably exceed rather than just emulate Strachan's contribution and fans' favouritism.
Indeed, he too must rank alongside Phil Jones, Jonny Evans and Wayne Rooney as future United captaincy material.