The Dons and the Glasgow club have already done business this summer, with Pittodrie favourite Jonny Hayes leaving for Parkhead on a three-year contract, while Ryan Christie has moved in the opposite direction for a second spell on loan in the north-east.
Because of the latter move, Mackay-Steven would be unable to join Aberdeen on a loan. Clubs in the same division can’t loan more than one player to each other in a season. Aberdeen will have to negotiate a permanent transfer.
Former Ross County, Liverpool, Airdrieonians and Dundee United wide-man Mackay-Steven has been at Celtic since February 2015 and has played in more than 60 games. However, he was used sparingly last season.
Sheffield United looked to bring the one-time capped player on board permanently during the summer. However, Aberdeen are hoping that the talks over the deal that were going on at the weekend will be completed in a matter of days.
Mackay-Steven would be unable to feature against Bosnian side NK Siroki Brijeg in their Uefa Europa League second qualifying round first leg on Thursday.
However, should the Dons progress, the deadline for registrations for the third qualifying round is 21 July.