Goal understands that Abramovich is reluctant to remove Mourinho now due to a lack of available replacements, with top targets Pep Guardiola and Diego Simeone unavailable mid-season.
Mourinho is under huge pressure with Chelsea sitting 16th in the Premier League table and many players understood to have turned against the Portuguese.
Last season’s champions have lost seven of their 12 league fixtures this season, the latest a 1-0 defeat to Stoke City on Saturday during which Mourinho served a one-match stadium ban.
Chelsea backed Mourinho with an unprecedented vote of confidence last month but have since lost three of their four Premier League matches and been knocked out of the League Cup.
Abramovich has been considering Mourinho’s future amid fears that the club will miss out on a place in next season’s Champions League given they are already 13 points off the top four.
The Russian billionaire is prepared to sack Mourinho but has decided to give him more time to turn Chelsea’s season around, with the Stamford Bridge hierarchy believed to have a number of reservations about making a change now.
The lack of an obvious replacement is the key issue, especially when there is a likelihood that Abramovich’s preferred targets could become available next summer.
Guardiola is out of contract with Bayern Munich next summer while Simeone is believed to be ready to move to the Premier League, with the Atletico Madrid coach and members of his backroom staff currently learning English.
But neither would join Chelsea midway through the season and nor would former Blues manager Carlo Ancelotti consider returning to west London before the end of the campaign. Guus Hiddink, a potential interim option, left his job as Netherlands coach in June during a poor Euro 2016 qualifying campaign.
Chelsea would also have to pay Mourinho and his backroom staff a significant severance package after he signed a £30 million four-year deal in August. It is unknown whether there are any financial clauses in his contract relating to the club’s qualification for the Champions League.
Mourinho is the most successful manager in Chelsea’s history and retains the vocal support of the club’s supporters, while he has insisted that he will not resign.
It means he will be given more time to turn the Blues’ season around but he is well aware that the boardroom consider current results and performances unacceptable.
Goal reported on Sunday that a significant proportion of the dressing room have turned against Mourinho and are feeling disillusioned.
The former Real Madrid and Inter coach has also found himself in hot water with the football authorities and received a one-match stadium ban and a fine after the 2-1 loss to West Ham in October.
Mourinho’s off-field conduct has been received badly in the Stamford Bridge boardroom, where there are concerns about the damage being done to the club’s image.
Mourinho faced heavy criticism after he publicly axed doctor Eva Carneiro, a popular member of the backroom team, earlier this season.
Carneiro is suing Chelsea for constructive dismissal and is also taking individual legal action against Mourinho.