Tchouameni, 26, has just begun his mandatory three-week break following France's run to the World Cup semi-finals. United are understood to have shortlisted him partly because he fits the club's preferred recruitment age range of 22 to 26, with the midfielder currently under contract at the Bernabeu until 2028.
Reports in Spain suggest he has already agreed to extend that deal to 2031, though Real Madrid have yet to confirm anything officially.
Crucially for Manchester United, Tchouameni operates as a specialist defensive midfielder, a profile distinct from summer arrivals Andrey Santos and Youri Tielemans. The club are still seeking an out-and-out No 6 to replace Casemiro, who was released this summer - a situation with a notable twist, given Real Madrid themselves turned to Tchouameni as Casemiro's long-term successor after the Brazilian's move to Old Trafford in 2022.
United's interest in the France international is not new. The club were offered the chance to sign him back in 2021, but were unable to meet the asking price for a midfielder at the time. Ole Gunnar Solskjaer, United's manager that summer, had instead prioritised a different long-term No 6, with Declan Rice his preferred target.
Whether the fresh contact with Madrid amounts to anything remains to be seen, particularly with reports of a new deal for Tchouameni gathering pace. But it underlines United's continued search for defensive midfield reinforcements as they look to build a squad capable of competing on multiple fronts next season.
Tchouameni has established himself as one of Europe's most reliable defensive midfielders since his move to the Bernabeu, forming part of a Real Madrid engine room that has helped the club challenge domestically and in Europe. Any deal to prise him away would represent a significant coup for United given his profile and standing within the France squad, though the size of any fee involved is likely to be substantial given his importance to Madrid's plans and the length of contract he already has in place.