Senior figures at Stamford Bridge are increasingly of the belief that the Italian is the man to succeed Andre Villas-Boas, BBC Sport understands. Several senior players are pushing Di Matteo's case, after just one defeat in his 15 games in charge of the Blues.
Technical director Michael Emenalo, who is overseeing the recruitment process, has already interviewed Di Matteo for the post, the Italian having guided Chelsea to the Champions League and FA Cup finals.
It has also emerged that the 41-year-old has been asked to make preparations for next season and help plan the club's pre-season tour of the United States, while Abramovich has promised Di Matteo a Â£750,000 bonus if he wins the Champions League.
BBC Sport understands intermediaries acting for Chelsea have also made contact with Real Madrid coach Jose Mourinho and Laurent Blanc, the France manager, to gauge their interest.
Chelsea midfielder Frank Lampard is among those backing Di Matteo. "I can't speak highly enough of him. Look at the record - it's not coincidence," Lampard said.
"He's created an atmosphere, a spirit and determination. What he's done in bringing it together and getting a result like this [the victory over Barcelona], and the results we've had before, is amazing."
The fluidity of the decision-making process at Stamford Bridge means nothing is guaranteed, however.
While Abramovich has been impressed by the way Di Matteo has gently shepherded a powerful, experienced squad through to the end of the season, he knows that is a very different task from the rebuilding that must still be done this summer.
The 41-year-old is considering taking a sabbatical from management at the end of what has been a tortuous season but will hold talks with Barcelona president Sandro Rossell before deciding whether to sign a new one-year contract.