German global Kroos is Mourinho's main target, though he may look to more than one player if club captain Michael Carrick does indeed retire at the end of the campaign and Maroaune Fellaini leaves the club on a free transfer, with Turkish giants Galatasaray heavily linked.
But, with Real believed to be preparing a squad overhaul in the summer, Kroos' future at the Bernabeu looks uncertain - and he is reportedly on a number of side's radars.
The usual pairing of Paul Pogba and Nemanja Matic was selected in midfield, with rumoured target Kroos playing in between them. But, Kroos has been the creative hub for Real Madrid, who have had to keep some of the biggest clubs at bay for the German global, including Manchester United.
However, the offer of a big-cash bid for Kroos - who is rated in the €80m (£72m) bracket by Real Madrid - could tempt them to sell.
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The United gaffer admitted last week that "we need to sign a midfield player... we need balance in the team", but if he does want Kroos he won't come cheap. You can accuse me of many things but you cannot say I lie to you.
"Some of you [the media] keep saying that we are going to buy that striker, that winger, that left winger, that right winger".
The Frenchman wants to play in a midfield three like he did with Juventus and Kroos is seen as the ideal selection alongside Matic and behind Pogba in the middle of the park. But I don't take you in other directions.