The Portuguese coach, who left the Blues after three years in 2007, is expected to leave Real Madrid at the end of the season following a number of reported disagreements with the Spanish club's board and players.
While Mourinho, who has revealed that he wants his next job to be in England, is thought to be on the shortlist to replace Rafael Benitez at Chelsea, Abramovich is believed to be unsure due to previous arguments between the pair.
"Roman is not sure of Jose because of the history between the two of them and what happened before," The Express quotes a source as saying.
"He is worried that the same things could happen again. He's still making up his mind."