Hearts need reinforcements up top with Kyle Lafferty having left the club for Rangers, and Sow would make a perfect fit.
He played for Hearts for two seasons between 2014 and 2016, before manager Robbie Neilson left Edinburgh for Milton Keynes and where the striker later joined him.
However, Craig Levein is keen to bring the Swede back before the transfer window closes in Scotland, and he revealed they are looking at a number of moves.
He said: "There are a couple of other things I'm looking at, and I'm confident when the window closes we'll be stronger than we are right at this minute in time."