Suso linked with AC Milan switch either in January or next summer
The 20-year-old has entered the final year of his current contract on Merseyside and is unsure whether he wants to extend that deal or not.
Milan manager Filippo Inzaghi is keen to bring Suso to the San Siro, either for a nominal fee in the New Year or on a free at the end of the season, according to the Daily Express.
The Spain Under-21 international has played just once for Rodgers in 2014/15 in the Capital One Cup and is frustrated at the lack of game time.