There has been substantial speculation surrounding the 18-year-old full-back, with interest from England and around Europe.
The Scotsman understands the club are yet to receive an offer for Ramsay, but do expect bids between now and the end of the window. However, the Dons are in a position where they are not required to sell.
For that position to change, a hugely attractive offer will have to be made for the player, one which would eclipse the £3million received for Scott McKenna from Nottingham Forest in 2020.
According to reports in Italy, Bologna are stepping up their interest, but it would have to involve the Serie A team making a sale to fund any move.
Aberdeen would be keen on the player returning on loan for the remainder of the season if a substantial offer was received, most likely from England.
Ramsay is understood to be very happy working and developing under manager Stephen Glass and his coaching team.
Earlier this month, Glass noted the club would not entertain bids very late in the window.
Meanwhile, one defender who could be leaving the club is Jack Gurr.
The 26-year-old has featured ten times since joining in the summer after leaving Atlanta United.
There is interest in the player from clubs in the United States and Aberdeen are allowing the player to make his decision on his future.