The MK Dons boss is keen to add some additional attacking firepower with his side sitting in 16th position in the League One table.
Hearts have previously admitted an interest in McGinn, who is a free agent following his exit from South Korean club Gwangju last month, and would be keen on signing the player if they can move some of the current squad on in the January window.
Manager Craig Levein, when asked about McGinn in November, said: “It’s a name that has been mentioned. I’ll need to look at what I can do to create some headroom. There’s loads of stuff going on in the background.”
Aberdeen are also believed to be interested in their former player, though that may change depending on the ongoing situation involving Derek McInnes and the vacant managerial position at Rangers.
McGinn starred at Pittodrie for five years before leaving for Korea under freedom of contract this past summer.