The 25-year-old, who is on a season-long loan from Old Trafford, will be out of contract at the end of the current campaign.
Everton are also been reportedly interested in signing the England international, despite manager Roberto Martinez refusing to be drawn on a potential deal.
However, Sherwood admitted Villa avoiding relegation could be crucial to his side being able to attract the player, with his side five points clear of the bottom three going into their final five league matches.
“I’ve been pleased with Tom,” said Sherwood. “I really like him and like what he adds to the side. He adds a lot of energy, gets back round goalside, links the ball very well.
“He certainly is one of the names I put on the team-sheet straight away. We’re certainly interested in talking to Tom, when the time is right.
“Tom and his representatives, and Aston Villa, are willing to put this on the backburner because they know how important it is to stay in the Premier League. After all Tom wouldn’t want to join the club in the Championship.
“I think there is a good chance we will try and do a deal if it’s right for both parties.”