The 24-year-old is in the final year of his contract at Tannadice but, with Ryan Gauld having already departed the club this summer, manager Jackie McNamara will not cash in on the Scotland international at this stage.
McNamara told STV on Tuesday: "We had a bid for him yesterday but it was rejected. That's as far as it is at the moment.
"I've spoken to Gary about it and said to him that I want to keep him here even though he's going to walk away for nothing next year.
"I don't think the offer was good enough for him or for the club."
McNamara would not reveal the bidders for Mackay-Steven, but Barnsley have shown an interest in him according to some reports.
Mackay-Steven, 24, joined United from Airdrie three years ago and has since made 106 appearances for the club and scored 22 goals.