The Swans saw Ben Davies move to Spurs earlier in the window, and they have yet to bring in anyone to replace the Welshman, though a move for Nice's Kolodziejczak is reportedly imminent report Sky Sports.
The 22-year-old Frenchman is set to move on after he missed Nice's first Ligue 1 game of the new season this weekend as a result of the speculation linking him with a move away from the club.
West Ham, Southampton, Queens Park Rangers, Bordeaux and St Etienne have all shown an interest as well as Swansea, and the French club's manager Claude Puel confirmed that a departure is likely.
"He is waiting for a departure, but as long as there is nothing definitive, we will see what we can do.
"He has expectation, but he is still a Nice player so far," Puel said.
Gary Monk will need to add a left-back before the end of the window and Kolodziejczak (commonly known as "Kolo") would be an excellent addition.
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The highly-rated Frenchman outperformed Davies in three key defensive areas last season as he won more tackles and made more interceptions and clearances per game than the Welshman.
Though Davies was more of an attacking threat as he picked up an assist, and created more chances for teammates than Kolodziejczak could manage.
If the Swans can wrap up a deal for the Nice defender, it will be an impressive acquisition as the young full-back looks set to have a bright future.
Would Kolodziejczak be a good signing for Swansea?