The 36-year-old is set to retire at the end of the season and will join Mourinho’s backroom staff after a trophy-laden 12 years at Old Trafford.
Mourinho is hopeful that Marouane Fellaini will sign a new deal so that he can use the bulk of his summer budget on obtaining a world class midfielder.
Kroos, 28, was close to joining the Red Devils on a free transfer in 2014 but Louis van Gaal’s appointment scuppered an agreement that was all-but in place under David Moyes.
According to the Independent, Real Madrid are planning a summer overhaul with a number of high profile exits and United are ready to test their resolve to keep Kroos.
The German is open to a move to the Premier League and his arrival would afford Mourinho the type of midfield that could see Paul Pogba thrive in a red shirt.
The Frenchman wants to play in a midfield three like he did with Juventus and Kroos is seen as the ideal fold ahead of Matic and behind Pogba in the middle of the park.
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Mourinho admitted earlier this month that he will sign at least one midfielder this summer.
‘We need to sign a midfield player,’ said Mourinho.
‘Because we are going to lose Michael Carrick. Of course, we need balance in the team.
‘Some of you [the media] keep saying that we are going to buy that striker, that winger, that left winger, that right winger.
‘You can accuse me of many things, but you cannot say that I lied to you. When I don’t want to say things, I don’t say [them]. But I don’t take you in other directions. We are looking and we are going to try to sign a midfield player.’