However, according to The Daily Express, the Blues’ new manager Jose Mourinho has decided to raise the amount of money he wants to offer for De Rossi from the initial figure of €11.5m.
The club are rumoured to be ready to listen to any offers at €17.5m or over, so Chelsea potentially stand a good chance of getting their man.
Mourinho had tried to sign the midfielder in 2006, during his first spell at Stamford Bridge, and was also interested in purchasing him at Real Madrid.
De Rossi met with Roma’s sporting director Walter Sabatini on Tuesday but no decision was agreed on regarding his future.
He is apparently eager to find out his place in the plans of recently-appointed coach Rudi Garcia.