Avram Grant has been axed by the Stamford club after chief executive Peter Kenyon claimed that "second best is not good enough for Chelsea."
The Blues' chairman, Roman Abramovich, is reportedly eager to build a new football project for Chelsea, which would always require the arrival of a major new coach.
And Rijkaard, who is looking for a new squad to coach following his departure from Barcelona, seems to be high on Abramovich's list to become the Israeli's successor at Stamford Bridge.
The British daily The Sun reports, meanwhile, that Chelsea are interested in the return of Portuguese coach José Mourinho, who left the club in September.
Nonetheless, La Gazzetta Dello Sport claims that The Special One has told Michael Essien that he will sign for Inter on Monday, which leaves Rijkaard in pole position to sign for the Premier League runners-up.
Whether Mourinho would even accept a return to Stamford Bridge is in itself a serious question.