The 26-year-old played in all five of Everton's opening games this season, before being sidelined by injury in their goalless draw with Tottenham Hotspur in August.
Everton are seventh following the 4-0 win over Aston Villa on Saturday, where Cleverly returned to the bench, three points and two places better off than they were at the same time last year.
"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," Cleverly told the club's website.
"Obviously, targets can change throughout the season but I think that is realistic for us at this point."
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The midfielder is equally sure that he would have played a part in England's Euro 2016 qualifying campaign this season were it not for his ankle ligament and groin injuries.
"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 (the England) fold, but these things happen," Cleverley said.
"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."
(Reporting by Simon Jennings in Bengaluru. Editing by Patrick Johnston)
