According to Simon Jones of the Daily Mail, Everton are ready to spend £8 million on a player Martinez had on loan at Wigan during the 2010-11 season.
Cleverley scored four goals in 25 appearances for the Latics, per Soccerbase, and Martinez is credited with improving the all-round game of the England international at that early point in his career.
And the Toffees manager is still a big fan of the 24-year-old midfielder:
Martinez (March 2014): "I think he [Tom Cleverley] is as good a talent as we have in the English game, and he is still growing"— GrandOldTeam.com (@grandoldteam) August 4, 2014
Cleverley's breakthrough season came in 2012-13 when he became an England regular and made 32 appearances for Manchester United, per Soccerbase. However, the following year he failed to kick on and became a scapegoat for the Red Devils' struggles under David Moyes.
His form and confidence did indeed drop and he failed to provide a single assist in 22 Premier League games last term, per WhoScored.com.
However, he has been given another chance under new coach Louis van Gaal in pre-season and was even named captain, ahead of Wayne Rooney, in a friendly against Roma during United's tour of the USA.
After running his eye over the squad in pre-season, Van Gaal is due to inform the players next week whether or not they will feature in his planned 22-man squad, per Simon Jones of the Daily Mail.
That decision will obviously be crucial as Cleverley believes he is a "Van Gaal type player" and would therefore naturally see his future at Old Trafford, rather than Goodison Park.
Cleverley told United's official site:
I watched the manager’s Holland team in the World Cup and from that I think I’m going to be his type of player. I have to show that in training and most importantly games. I think there’s a place for me but I have to prove it.
However, following the arrival of Ander Herrera from Spanish side Athletic Bilbao earlier this summer and United's continued pursuit of Juventus midfielder Arturo Vidal, per Charles Perrin of the Daily Express, there are sure to be player sales from a midfield that underperformed last season.
Having impressed former Manchester United manager Sir Alex Ferguson and England bosses Fabio Capello and Roy Hodgson, it is clear that Cleverley has something about him.
A move to Everton and a reunion with a manager who showed faith in him as a young player might be the perfect match.
Martinez revitalised former Manchester City midfielder Gareth Barry—a not-too-dissimilar player—at Goodison Park last season. Few would bet against him doing the same with Cleverley.