Swansea are in the market for a new left-back after selling Ben Davies to Tottenham earlier this summer.
Highly-rated full-back Kolodziejczak has been linked with a move to England all summer with the likes of West Ham, Queens Park Rangers and Southampton all credited with an interest in the 22-year-old.
Bordeaux and St Etienne are also chasing Kolodziejczak, with Nice resigned to losing the former France Under-20 international.
Kolodziejczak has been left out of Nice's squad for this weekend's opening Ligue 1 game with Toulouse as coach Claude Puel feels he is not in the right frame of mind of play as speculation surrounds a possible move before the close of the transfer window.
"He is waiting for a departure, but as long as there is nothing definitive, we will see what we can do," said Puel.
"He has expectation, but he is still a Nice player so far."