The midfielder has returned to full fitness following an injury at the end of August.
The midfielder joined Roberto Martinez’s side on a free transfer in the summer, with his contract at Manchester United having come to an end.
However, it has not been an ideal start to life at Goodison Park for him, with an ankle injury picked up against Tottenham ruling him out since the end of August.
The side have done well in his absence, sitting six points outside of the top four and very much eyeing up those Champions League places.
And Cleverley says he is eyeing up those European spots, as well as a potential cup run, with them currently in the quarterfinals of the Capital One Cup.
“The fixtures we have had so far and the results we’ve got from them shows there is no stopping us finishing in one of the European spots,” he told evertonfc.com.
“Obviously, targets can change throughout the season but I think that is realistic for us at this point. It is [also] really important to me and all of the other players that we really do try and get to Wembley.”
He also says he hasn’t given up on a potential place in the England squad for Euro 2016.
Manager Roy Hodgson has handed a number of players their England debut this season, having lost several of his more regular faces through injury.
Cleverley has found himself unfortunate to be injured then, having been a part of squads in the past, and he says he focus on doing well for Everton and hoping that gets him into the England squad.
“It’s been playing on my mind for 10 or 11 weeks now while I’ve been out that I could have really got back in that fold, but these things happen,” he added.
“I’ve just got to get my head down now and first of all get myself back in the Everton team and play well for Everton. Hopefully the England call can come as a result of doing that.”