Our source revealed: "Frank has spent four years at Barca and he gives the impression that he wants a new challenge.
"Chelsea is one of the options available to him. He will make his plans known at the end of December."
Although current Blues boss Avram Grant signed an improved deal last week, that was seen as a ?thank you' from Abramovich to the Israeli coach for steadying the ship after the shock departure of Jose Mourinho.
The billionaire Chelsea owner would still like a high-profile coach with a proven record - and Rijkaard fits the bill.