Last summer, the Red Devils added Eriksen and Casemiro to their midfield, as well as Marcel Sabitzer on loan for the remainder of the season.
Erik ten Hag, on the other hand, is looking at Valverde, who has the potential to push United to the next level next season.
According to the Spanish newspaper Nacional, Manchester United has made a £58 million proposal for the Uruguayan international, who has struggled for form recently.
Valverde was a key figure in Real Madrid’s title-winning season last year, appearing in 49 games across all competitions. He also assisted on Liverpool’s winning goal in the Champions League final.
The 24-year-old has six goals and two assists in 20 La Liga appearances this season under Ancelotti.
However, despite a strong start, his record has plummeted considerably since the World Cup, with no goals or assists in his past eight appearances.
However, this has not deterred United or Ten Hag, who is said to be a big fan of the midfielder, hence the decision to launch the £58m bid, according to sources.
Valverde has the potential to make United unbeatable.
The Uruguayan international has 47 caps and can press efficiently, break up play, make excellent runs into the box, and strike the ball strongly with either foot.
Valverde has 15 goals and 12 assists in 180 outings across all competitions since joining Real Madrid in 2018.
He also helped his team win two La Liga crowns, a Champions League, a FIFA Club World Cup, a UEFA Super Cup, and two Spanish Super Cups.
With that in mind, the midfielder might help bring a winning mindset to United’s locker room as Ten Hag strives to rebuild the club into a serial-trophy winner once more.
While Eriksen and Casemiro are both outstanding players, they are both 30 years old, whereas Valverde may be a more long-term choice for the Dutch manager.
Liverpool reportedly had an £80.4 million proposal for Valverde rejected last summer, so they might re-enter the race for the midfielder.
However, it is reported that Jurgen Klopp has made signing Borussia Dortmund’s Jude Bellingham his top goal, making it doubtful that they could pay both players.
This leaves United as the most likely candidate to sign Valverde, but only if Real Madrid decides to sell him.
While he is now out of form, Ancelotti is fully aware of his talent, and it appears doubtful that he will allow him to depart for £58 million.
The Uruguayans’ current contract at the Bernabeu runs until 2027, so they are under no obligation to sell. With that in mind, a bid of around £100 million is more likely.