The Nigerian is yet to feature under Antonio Conte this season after falling down the pecking order.
Despite 10 trophy-laden years in west London, the 28-year-old's contract expires at the end of the season and there are no plans to hand him a new deal, The Sun claim.
And the report suggests Mourinho, who was a big fan of Mikel during his time with the Blues, is keen to take advantage of the situation by bringing him to Manchester United in a cut-price deal.
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He is confident of making a move for him in January and wants the midfielder to work alongside Paul Pogba.
And Mikel even admitted he could move elsewhere in the New Year.
He told BBC Sport: "I will keep doing my best and ready for when called up upon," he said. "We will see what happens in January."
The report suggests Mourinho is also keeping tabs on £30m-rated Leicester star Danny Drinkwater.
The talented midfielder played a key part in Leicester's incredible title-winning campaign last term, but they have struggled to replicate the same kind of form this season.
However, with the Foxes qualifying for the knockout stages of the Champions League, Mourinho is well aware it'll be a tough task to prise him away from the King Power Stadium in January and a move in the summer would now be more likely.