The Russian is believed to have patched up his indifferences with the current Real Madrid manager and is keen to lure him back to London at the end of the season.
The duo split on bad terms in 2007 but wages of more than £9m a year, and a compensation bill from Madrid of £25m, would be sanctioned by Abramovich, according to The People.
A Chelsea source is quoted as saying: "Such is Roman's determination to bring back Mourinho that he is prepared to top Jose's Madrid wages and pay compensation to buy out the remaining two years of his contract."
Whilst Mourinho is Abramovich's first choice the shortlist for the manager's job is completed by France coach Laurent Blanc, Marseille boss Didier Deschamps and Zenit St Petersburg's Luciano Spalletti, who are also in the frame if the Real Madrid chief cannot be persuaded to return to Chelsea.
The newspaper also reports that interim boss Roberto Di Matteo will receive an interview for the Chelsea manager's job if they overcome Barcelona in the Champions League after their 1-0 win in the first leg on Wednesday.