And the bid for the Belgian midfielder is also thought not to signal the end of the club’s pursuit of Barcelona star Cesc Fabregas.
United are expected to formerly submit a joint bid in the coming days, with Moyes still in search of his first marquee signing since arriving at Old Trafford officially on July 1.
Moyes has previously seen an offer of £12million for Leighton Baines rejected out of hand by Everton, but is now willing to test his former chairman Bill Kenwright’s resolve, with a hefty bid for both players.
The United boss has still not ruled out the possibility of making a third offer for Fabregas, and is said to be constantly monitoring the situation.
The Spaniard is set to reveal his true intentions at a press conference on Thursday, while Fellaini is known to be desperate to complete the move to Old Trafford.
The Belgian powerhouse is keen to be reunited with Moyes, the man who brought him to the Premier League in 2008.
Moyes has come under fire for his failure to make any signings so far, and has admitted he has at times found it difficult to make the step up in the past five weeks.
“The transition from Everton to United has been difficult at times as I have hard decisions to make,” Moyes said.
“Everton are a great club and I was proud to manage them. But I can’t deny Manchester United is on another level. Let’s be honest, it would be a step up from just about any club in the world.”
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