It is being reported by Italian radio station Radio
The bid is believed to be in the region of 11.7m Euros, and the Blues were originally thought to be preparing a 10m Euro offer, but Mourinho has upped the ante in a show of desire to get his man.
With some newspapers reporting that the Stamford Bridge outfit have a £100m transfer kitty to play with, the 29-year-old looks to be topping their Portuguese bosses’ wish-list as part of a new look Chelsea. It may be difficult to prise De Rossi away from the Italian capital though, as he has been a one club man thus far in his career.
The defensive midfielder, who has made over 300 appearances for Roma over his career, had also piqued the interest of Manchester City, but it is thought that Manuel Pellegrini is more intent on capturing his targets Pablo Osvaldo and Alvaro Negredo before looking at any other players.
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