Since his appointment on an interim basis following the sacking of Andre Villas-Boas in March, the former West Brom coach has rejuvenated the Blues, leading them to victories in the finals of both the FA Cup and the Champions League.
And, while Abramovich does not view Di Matteo as a top class manager, he has accepted that the 41-year-old deserves a further opportunity at Stamford Bridge after his remarkable achievements this season.
However, any decision is unlikely to be reached until next week, meaning the former Blues midfielder will depart for his preseason holiday with his future still undecided.
The ex-MK Dons boss is believed open to the prospect of a 12-month deal though, having only forced his way into consideration thanks to his Champions League success.
Although the Italian has the backing of the club’s squad and fans, their owner still retains hope of luring former Barcelona boss Pep Guardiola to west London, following the Spaniard's sabbatical from the game which begins this summer.
- Roman Abramovich