Chelsea, meanwhile, have done the same - beating Manchester City to the £50million signing of Jorginho from Napoli.
United’s midfield is well-stocked with Paul Pogba, Nemanja Matic, Marouane Fellaini, Ander Herrera, Scott McTominay and Fred all on the books.
Over at Chelsea, and Maurizio Sarri has Cesc Fabregas, N’Golo Kante, Tiemou Bakayoko and Jorginho to call upon.
But ESPN say the two clubs are leading Barcelona in the race to lure Thiago away from Bayern this summer.
Meanwhile, speaking back in May, Thiago admitted he was unsure of his future in the Bundesliga.
Man Utd nearly signed Thiago from Bayern Munich while Jose Mourinho was at Chelsea (Image: GETTY)
Bayern Munich: Thiago Alcantara shows off incredible skill
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The Spain star said: "Let's see. I told you I renewed with Bayern last year, but it's very complicated. Football is very difficult...
"I'm very much about enjoying the moment.
“You don't have to focus on the future. Now, I'm thinking about the World Cup, I'm living in the present and if a moment comes for you to think about it, I immediately focus on the World Cup."
Thiago has won the Bundesliga every year since joining Bayern from Barcelona in 2013.