The Sun says England ace Cole is facing an uncertain future under boss Kenny Dalglish despite playing a full part in pre-season.
And big-spending PSG - now backed by the Qatar Investment Authority - believe they could get him out of Anfield on a free transfer to get his £90,000-a-week wages off the Kop books.
Cole, 29, has told pals he is ready to accept a move abroad if a switch to a top Premier League club does not come off.
Spurs are keen, but boss Harry Redknapp must unload a few players before he can buy.
Premier League new boys QPR have also been linked with a daring move but Cole has told pals he still believes he can play at the very top level.