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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.