Moyes' Everton teams were built upon the solid foundations of a well-drilled defence. The Scottish manager will be keen to continue that tradition in his new role at Manchester United.
In the short-term, Varela may well be loaned out to gain more experience, but Moyes will be on the look-out for more experienced defenders who can immediately improve the United defence.
Go to the next slide to see the first of five possible targets who could instantly bring security and style to the Old Trafford back line.
Manchester United's most famous achievement is arguably the historic treble of 1999. In 2012/13, Ezequiel Garay's Benfica suffered an inverted treble of horrors, losing the league, domestic cup and Europa League to a hat-trick of late goals.
That's no reflection on Garay's own performances. Alongside big Brazilian Luisao he formed an impressive defence that almost carried Benfica through the entire season unbeaten. His performances didn't go unnoticed, with the Mirror suggesting he may be United's main defensive target.
Garay has already moved to one of European football's elite clubs. In May 2008 he signed for Real Madrid, but he found his opportunities to start limited and eventually moved on.
If he is given the opportunity to play for another giant of world football, he will be desperate to seize it with both hands.
In March, Porto's 6' 2" centre-half, Eliaquim Mangala, was quoted by the Express as saying:
To be linked with clubs of the stature of Tottenham or Manchester United is the best feeling.
I want to finish the season strongly and see at the end of the season if the reports are true.
Mangala did finish the season strongly, helping Porto pip Benfica to the Primeira Liga title and making his international debut for France against Uruguay.
If United want to secure the fleet-footed Mangala, they may have to move fast. According to the Mirror, Jose Mourinho has edged ahead of David Moyes in the race for his signature.
With doubts remaining over Patrice Evra's long-term future with the club, Everton's Leighton Baines could be the perfect replacement.
The Daily Mail claim that David Moyes would like to make his former charge his first major signing, and it's easy to see why.
Last season Baines excelled, providing Ashley Cole with genuine competition for England's left-back spot. On the domestic front, his partnership with Steven Pienaar was one of the most exciting in the Premier League.
Baines would hope to replicate that understanding with either Ashley Young or Shinji Kagawa on United's left flank.
The likes of Robin van Persie and Javier Hernandez would certainly welcome the arrival of a player who racked up five Premier League assists in 2012/13.
The Sun have linked Manchester United with a move for another one of David Moyes' former charges: Phil Jagielka.
Jagielka has come a long way since the days of being Sheffield United's utility player and occasional reserve goalkeeper. He is now a regular for the English national team, with 18 caps to his name. Earlier this month, he started alongside Gary Cahill in the draw with Brazil, performing impressively to shackle the likes of Neymar and Hulk.
Jagielka has already taken over Rio Ferdinand's spot in the England team and could be primed to do the same at Old Trafford.
According to The Express, Manchester United are battling it out with Barcelona for the signature of Borussia Dortmund's Teutonic titan Mats Hummels.
Hummels was a key component of the Dortmund side that made it all the way to the Champions League final, forming an effective partnership with the similarly imposing Neven Subotic.
However, Hummels will be alarmed that the Dortmund side is dismantling around him. Mario Gotze has already agreed to join Bayern Munich, and Robert Lewandowski was, until recently, widely expected to follow suit. If the Dortmund ship isn't quite sinking, it has certainly sprung a leak.
United could seek to take advantage by securing one of Europe's most highly rated defenders. Hummels is powerful in the air and accomplished on the ball and would be an excellent partner for any of United's existing centre-backs.
Which of these five defenders do you think would add most to United's back line?