The Sun says Chelsea are going for the Brazil international as fears grow that Frank Lampard will refuse to sign a new contract at the end of this season.
Last season's Bundesliga Player of the Year scored Brazil's injury-time equaliser in the friendly against England at Wembley nine months ago.
He is under contract to 2011 but Bremen - second in the German league - will find it difficult to refuse a big-money offer.
An insider said: "There is a lot of talk going on around the club about Diego.
"There is loads of interest across Europe but Chelsea are the most likely to come up with the money."