The report claims Roma will now consider offers for De Rossi after all but agreeing to the signing of Strootman.
The Serie 'A' club are believed to want £11m plus a season-long loan deal for Chelsea's latest Brazilian recruit Wallace. The full-back was signed by the Stamford Bridge club last season from Fluminense in a £4m deal.
Jose Mourinho is a huge fan of De Rossi, having twice tried to sign him before when manager of Inter Milan and Real Madrid.
With John Obi Mikel linked with a move to Turkey, the Chelsea boss sees the 29-year-old Italy international as the perfect man to step into the role at the base of the Blues midfield.
Roma wanted a like-for-like replacement before agreeing to negotiate on the sale of De Rossi. And the report claims PSV technical director Marcel Brands has agreed a £15m fee, allowing Chelsea to push ahead with a move for the Roma star.
The PSV official stated earlier this week that the Dutch international midfielder is not for sale, although he conceded an "important offer" could bring them to the negotiating table.
The report claims Chelsea have already got a four-year contract worth close to £110,000-a-week in place for De Rossi.
Mourinho is looking to reshape Chelsea's midfield, with Marco van Ginkel already brought in from Vitesse as a long-term successor to Frank Lampard.
De Rossi would provide another experienced campaigner to play in an otherwise young attack boasting the likes of Andre Schurrle, van Ginkel, Eden Hazard, Oscar and potentially Romelu Lukaku.
Chelsea leave for their pre-season tour of the Far East on Thursday.