The Roma midfielder has previously pledged his loyalty to the Italian side, but RMC report that the two teams are in talks about a move.
De Rossi could replace Momo Sissoko, set to leave Paris to join Fiorentina.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.