According to the Daily Mirror, Monaco owner Dmitry Rybolovlev has already been in contact with Mourinho's advisers, including agent Jorge Mendes, giving a presentation for the Portuguese on his plans for the principality club.
Mourinho is said to have set a price of £12m per season to return to Chelsea and Rybolovlev is capable of paying that sort of money - indeed, the newspaper claims he is willing to top any offer from his compatriot Roman Abramovich, the Chelsea owner.
Monaco have also been linked with a move for Manchester City manager Roberto Mancini, and are currently led by Claudio Ranieri, who, ironically, was also Mourinho's predecessor at Chelsea.
Currently top of the French second division - Ligue 2 - Monaco are understood to be willing to lavish money on transfers in order to build a side capable of competing both at home and on the continent, perhaps rivalling fellow wealthy club Paris Saint-Germain.