The Tannadice outfit have made a move for their former player who is still recovering from the ankle surgery he underwent in the summer.
Ross County have also been linked with an attempt to secure a loan deal for the ball-playing artist who began his career as a youth player in Dingwall before joining Liverpool in 2007.
Mackay-Steven made 37 appearances for the Hoops last season under Ronny Deila, scoring six goals.