The Portuguese, who led the Blues to the Premier League title last season, is said to be under huge pressure with the club now 16th in the Premier League with just 15 points from their first 15 matches, a point above the relegation zone.
Mourinho still retains strong support from the Chelsea fanbase but Russian billionaire Abramovich will hold talks with his closest advisors at the club, according to the Daily Mail.
Chairman Bruce Buck, directors Marina Granovskaia and Eugene Tenenbaum and technical director Michael Emenalo are expected to be at the meeting.
Mourinho, who received the public backing of the board earlier this season, signed a new four-year deal in the summer after winning the title and is currently the highest-paid manager in the Premier League with an annual salary estimated at anywhere between £8m and £13m.
His new deal did not contain any buy-out clause, meaning Abramovich would be forced to pay a fortune to sack him from Stamford Bridge. Mourinho has reiterated his desire to stay in charge and would likely demand a full compensation package that is estimated to be in the region of £40million.
That huge price, plus a lack of realistic alternatives could keep Mourinho in his job for the time being.
Abramovich, who was at Stamford Bridge for the 2-0 Champions League win over Porto last week, is also keen to shake the reputation he has for lacking patience with managers.
The Independent revealed earlier this month that Antonio Conte is the leading candidate to replace Mourinho, but he is under contract with the Italian national team until the end of Euro 2016.
Carlo Ancelotti does not want to take up any job mid-season, leaving Brendan Rodgers as the only realistic candidate on an interim basis.
“I want to be [the manager],” Mourinho said after defeat to Premier League leaders Leicester City. “I have no doubts and you know me well enough that I’m not afraid of a big challenge. It is a real big challenge and I want to stay. I hope Mr Abramovich and the board want me to stay. I would like the board to analyse the situation, the budget, the balance of the club and what they were expecting.”
Chelsea legend Frank Lampard believes Abramovich would be wrong to sack his former boss.
“He’s probably looking at it very closely,” he told Sky Sports. “Obviously we’ve been here before with Chelsea when managers change midway through the season.
“I don’t know how many times you can do that. We had some good results from doing it before but we had a different set of players at that point.
“But I have to say what they set out to do when Jose Mourinho came back was to have a long-term plan. What can they gain by getting rid of him now?
“They are probably not going to make the top four anyway or the top six. They’re not going to get relegated I think if we are honest so I’m sure there’s a view from Roman Abramovich to say, ‘Hang on, let’s see what happens at the end of the season’.
“Why make a rash change that can’t really affect the year that much and then see where we are at the end of the year.”