The 27-year-old has been at Manchester United for his entire career so far, although he looked likely to be leaving a year ago.
The midfielder appeared to have fallen down the pecking order at Old Trafford and West Ham were interested in signing him, but saw a £30m bid rejected.
McTominay stayed with the Red Devils and due to a number of injuries to his teammates over the campaign he featured regularly, making 43 appearances in all competitions and scoring 10 goals.
The Scotland international was in the starting line-up as United stunned Manchester City to win the FA Cup final in May.
A sale of McTominay this summer looked much less likely than last, but Galatasaray’s vice-chairman has suggested that it is very much a possibility.
Ibrahim Hatipoglu told CNN Turk: ‘We are interested in a player from the Premier League and Manchester United.
‘There is nothing more natural than the high cost of this. There are discussions regarding his transfer fee. For us, the total cost, including transfer fees and player receivables [salary], is important at the decision point.
‘Once the negotiations with both the club and the player are completed, the cost becomes apparent.’
Giving away more detail he said, via Haber Sarı Kirmizi, that Tottenham’s Pierre-Emile Hojberg is also a target.
‘McTominay’s transfer is being discussed,’ said Hatipoglu. ‘Pierre-Emile Højbjerg is a good player, he has many suitors, he wants to see all options.’
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