French newspaper Courrier Picard claims that the Ibrox side have scouted the 23-year-old, but face competition from La Liga side Espanyol, who have also made regular visits to run the rule over the player.
The 6ft 2in forward, who can also operate on the left flank, only joined the Ligue 1 side on a permanent deal for a reported fee of around £5.4 million in June, after initially signing on loan in January from German club FC Koln.
Guirassy, whose parents hail from Guinea, only played 45 times for the Billy Goats and was hampered by injuries during his time in Germany.
The former France Under-20 international also has experience with Stade Lavallois, LOSC Lille and Auxerre in the French top flight.
So far this season he has netted four goals and registered one assist in 13 matches. He is under contract with the French side until 2022.
The Courrier Picard reports that Guirassy, along with Alfredo Morelos' Colombian international team-mate Stiven Mendoza, could be on the move as soon as next month.
Meanwhile, the Light Blues have also been linked with a January move for Portsmouth and Scotland goalkeeper Craig MacGillivray.