It is anticipated interim manager Stuart Pearce will hand a number of inexperienced players their chance when he unveils his squad. That speculation was given credence by confirmation Joleon Lescott will not be involved, even though fellow central defenders John Terry and Phil Jagielka have been ruled out through injury.
Cleverley, still to make his debut despite two call-ups to senior ranks earlier in the season, said: "If I can find some good form from now until the end of the season, I would be more than happy to be involved in the European Championships."
The 22-year-old added: "I know Stuart Pearce quite well from my time with the Under-21s. He is a good manager. Hopefully I will be involved."
It had been anticipated Lescott would also be included.
However, following Wednesday night's Europa League victory over Porto, the Manchester City defender confirmed he will not be involved.
"I have been told I am not involved," said Lescott. "It is a chance for other players to get involved and prove what good players they are."
In addition to Cleverley, Arsenal's Alex Oxlade-Chamberlain is the most likely uncapped player to make his international bow.