However, the pursuit faces significant obstacles on both price and availability.
Transfer journalist Fabrizio Romano, speaking on his YouTube channel, confirmed the extent of United's interest.
"If you ask me who is the dream internally in terms of defensive midfielder for Casemiro's position, I could mention Tchouaméni. They see another Casemiro in him — not only because he would come from Real Madrid, but also in terms of skills and leadership. They love Tchouaméni at Manchester United."
He was equally clear about the difficulties.
"Tchouaméni is a really important player for Real Madrid right now. The doors are not open for a Tchouaméni exit — Real Madrid trust him. And his salary is a very, very significant salary. So it is not easy at all."
Casemiro departs Old Trafford this summer as a free agent, ending a four-year stint. Manuel Ugarte is also expected to leave, meaning Michael Carrick may need two midfield additions before the start of next season.
Tchouaméni, 26, joined Real Madrid from Monaco in 2022 for around £80 million and has established himself as one of the best defensive midfielders in Europe. He made 40 appearances across all competitions this season, contributing six goals, and is in France's World Cup squad for the tournament in North America.
His salary at the Bernabéu is reported to be in the region of £200,000 per week — a figure that would require significant structural flexibility from United's wage budget to accommodate. Real Madrid's valuation would likely begin at around £80 million given his contract runs until 2028.
Sandro Tonali of Newcastle United remains Carrick's primary midfield target, with Ederson of Atalanta also close to agreement. Tchouaméni represents the more ambitious alternative — the one United want most and are least likely to get.