Following successful loan stints with Watford and Wigan Athletic, 25-year-old Cleverley made an initial impression on the United senior side when given the opportunity by Sir Alex Ferguson in 2011.
However, in what was a difficult campaign for the club last term, Cleverley received a hefty amount of criticism for his performances, which resulted in him deactivating his Twitter account in February, while a selection of England fans started a petition against the midfielder being a part of the Three Lions squad that went to the World Cup.
It had resulted in reports that he could leave United this summer, but BT Sport pundit Savage has claimed that he may still have a future at Old Trafford, but only if he enhances a particular aspect of his game.
"He's obviously a very good player. For anyone to play for Manchester United, you have to be very good. You don't come through the ranks at Old Trafford, break into the first team on a regular basis and play for England if you don't have something about you. People that say he is rubbish, that is a load of nonsense," Savage told Sports Mole.
"He needs to add something to his game, though. Something like scoring more goals, winning more tackles or improving his range of passing. To be at the top echelons of that club, one part of your game has to be outstanding.
"Paul Scholes scored goals from midfield, you could never get past Roy Keane because of his desire and Bryan Robson - what a player he was. For Tom Cleverley to get anywhere near that, he needs to distinguish one aspect of his game, but at the minute he's good at most things, but outstanding at none.
"When people were drawing up petitions for him not to play for England, that was absolutely ludicrous and of course that is going to knock your confidence. I was a critic of him last year on Match of the Day because I want to see him do better, which I think he will under Louis van Gaal if he gets the chance."
Cleverley, who joined United as a trainee in 2000, has recently been linked with a switch to Everton.
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