Monaco looked to steal a march on landing Mourinho and offered to buy out his contract when shareholder Alessandro Proto met Chelsea owner Abramovich.
The Russian rejected the £35m offer on a day his manager insisted he would remain in London until 2019.
It represents a strong show of faith from Abramovich, who had been urged to dispense of Mourinho after six League defeats with the champions lying 15th.
A statement was released by Proto’s company, Proto Enterprises, to a Spanish news agency stating the meeting had taken place in London earlier in the day.
Proto Enterprises confirmed its authenticity to Sportsmail on Tuesday night and alleged Abramovich could be interested in accepting should they double the offer to £71m.
Asked how much time he thought he left, Mourinho, who signed a new contract until June 2019 on the eve of the season, said: ‘Four years. In this case, three years and seven months.’