Roma sporting director Franco Baldini has admitted his club would entertain offers for the Italy international, with Chelsea and Manchester City reportedly interested, but that did not necessarily mean the Italian club would accept the bids.
According to the report, Manchester City had a €50m offer turned down, but the 52-year-old Baldini revealed fresh bids would have to be considered.
"In the summer there was an offer made by Manchester City," Baldini told Sky Sport Italia. "We listened to that offer and considered it.
"If we were to get another offer we would listen again. But we could easily decline again."
The 29-year-old has spent his entire career with Roma, and is one of Serie 'A''s best players. Chelsea and Manchester City were reportedly battling for the midfielder's signature earlier last month, after De Rossi seemed to fall out of favour under Roma coach Zdenek Zeman.
The Czech boss took over at the Rome-based club this summer, but De Rossi has only started six games this season, and ESPN reports some members of the club's board would be keen to cash in on the Italy star in January, with Chelsea and City the most likely destinations.
ESPN also suggest Real Madrid and Paris St Germain are interested in the Chelsea and City target, but De Rossi is under contract with Roma until 2017.