Chelsea manager Jose Mourinho is reported to have tried to sign the Italian international during his stints in charge of Inter Milan and Real Madrid, but on both occasions the midfielder opted to stay put.
However, having turned down Manchester City 12 months ago, the 29-year-old is now more open to a switch to England, according to The Mirror.
A source close to Roma and De Rossi said: "If Mourinho calls, I'm sure De Rossi will say yes.
"He did not want to go to Manchester City, but Chelsea are the club who could take him to England. If Chelsea are prepared to pay his wages, then it is a transfer that can happen."
It is believed that De Rossi currently earns around £5.5m a year.