The Blues have been chasing Roma defender Emerson Palmieri, but top Italian journalist Gianluca Di Marzio has claimed that deal is in jeopardy.
Kurzawa began his career at Monaco in 2010 and went on to make almost 100 senior appearances for the club.
He joined PSG for €23 million in 2015, winning a treble in his first season.
The 25-year-old has scored 11 goals in 69 appearances for PSG and the French giants are understood to be reluctant to sell him during the season.
Chelsea had been aiming to complete a double swoop for Palmieri and striker Edin Dzeko, but both transfers have proved difficult to complete.