The 31-year-old's mum, Sue Cole, has told Facebook pals: "Well looks like his going somwhere better hear than the talk of man u. Not too far on the Euro star x," The Sun reports.
According to the paper, Cole has failed to agree fresh Chelsea terms after being offered only a one-year deal and PSG are set to win the race to sign him.
Manchester United have also been interested in the England defender, who will be available on a free in the summer, the paper said.
Sue also posted a link to a report that PSG boss Carlo Ancelotti had already made contact, the paper added. (ANI )