The 21-year-old, who spent last season on loan at Wigan, enjoyed his first full 90 minutes of pre-season in the USA as United beat Barcelona 2-1 in Washington DC.
With Paul Scholes retired and Darren Fletcher still fighting his way back to fitness, there could be an opening in central midfield at the start of the season.
And, after a mature performance against the European champions, which included an assist for Michael Owen’s winner, Cleverley is certainly in the manager’s thoughts.
“With Paul Scholes retiring and Darren Fletcher still recovering from his virus, [central midfield] is an area we have to find a solution for,” Sir Alex said.
“Tom Cleverley, physically, isn't the strongest lad but he's wily and he has a great idea of the game.
“He's a good footballer and I thought he was our best player [against Barcelona]. His discipline was terrific, he's a good passer and he has good eyes.
“He's a big possibility to start for us at the start of the season.”
Cleverley enjoyed his run-out against the Catalan giants.
“It’s nice to test yourself against some of the best players in the world,” he told MUTV.
“This was a big game for me and the other fringe players trying to stake a claim. There were a