The 31-year-old is under contract at the Parc des Prince until 2015 but talks over a renewal are said to have stalled, with both parties 'far apart' in their demands according to the Italian publication.
That has opened up the possibility that the midfielder could be on his way out of Paris, with the likes of Juventus, Real Madrid and Chelsea said to be interested.
According to Tuttosport, Juventus's interest in the former Inter Milan and Barcelona star is long-standing. The Italian club reportedly see him as the ideal replacement for Andrea Pirlo when he eventually decides to retire from the game.
Chelsea boss Jose Mourinho is said to be open to the idea of taking Motta to Stamford Bridge in January.
Together the pair won the Champions League with Inter Milan in 2010, and Mourinho is said to be 'closely' following Motta's situation ahead of the transfer window.
Real Madrid are also in the hunt, and could step up their interest if Xabi Alonso decides his future lies away from the Bernabeu.