The midfielder was one of the most impressive performers in the Premiership last season and became a big fan favourite at Tannadice on loan from the Red Devils.
Levitt netted six goals in 29 appearances, including fine strikes against Celtic and Hearts.
United sporting director Tony Asghar confirmed to the Sunday Mail the club are in talks with Manchester United about bringing the 21-year-old back to the club.
Levitt, who will be hoping to be part of the Wales squad at the World Cup in Qatar, had been linked with a switch to Derby County before Wayne Rooney departed the League one club, while Cardiff City have been credited with an interest.
“We’re still interested and talks are ongoing,” Asghar said. “He’s just got another year with Manchester United and he’s got a World Cup to aim for, to try and get into the Wales squad.
“Dylan is a player who fits into our system. He is well liked by all of the players and loved by the fans.
“So yes, we are still trying to see if we can do something there."
United appointed former Hibs boss Jack Ross as their new head coach following the departure of Tam Courts to Hungarian side Honved.
As of just now, they are the only team yet to sign a player while they are still waiting to tie Ian Harkes down to a new contract.
Ross, who has been linked with Hibs striker Christian Doidge, is expected to be busy in the coming days and weeks.
“Jack likes the player,” Asghar said. “When you bring a new manager in, you have to run the list of targets past him.
“With Jack, I think we know we are on the right track with targets. When you see Levitt and the influence he had, especially in the second half of the season, he is a player we would like at Dundee United. But right now, he is a Manchester United player. We are speaking to them and they know our feelings.
“Dylan is a player we would like to have but it’s going to take United and ourselves to come to an agreement.”