Cleverley played on loan for Villa from Premier League rivals Manchester United in the recently concluded 2014-15 season.
The England international midfielder will become a free agent at the end of this month when his current contract with United runs out.
However, the former Tottenham Hotspur manager has admitted that it is up to the midfielder to decide his future, and has suggested that he has a few other options.
“I have told him I want him to stay,” Sherwood told The Guardian. “We will have a chat with his representatives and see if we can get a deal done.
“I would have thought Tom would have had a few options. He’s enjoyed his time here. I think he has flourished and it is up to him.”
Cleverley had a good 2014-15 campaign with Villa and was one of the team’s most important players.
In 31 Premier League appearance, the Englishman scored three goals and created 26 chances.
Cleverley had a pass accuracy of 86% and a shot accuracy of 56%, and he won 11 headers, nine dribbles and 58 tackles.