David Moyes has made a €30m (£26m) bid for Cesc Fábregas and could pair the Barcelona star with Everton's Marouane Fellaini to form the heart of his Manchester United midfield next season.

Moyes has identified the need for two midfielders, at least one of whom must be able to contribute goals, which Fábregas has proved he can do in the Premier League when at his former club, Arsenal. Fellaini also has an eye for goal; he scored 12 times for Everton last season.

Moyes considered Real Madrid's Luka Modric before deciding on lodging an official offer for the former Arsenal captain. The deal hinges on whether Barcelona – who purchased the player from Arsenal for €29m (£25m) in 2011 – are willing to sell.

Publicly they have maintained the midfielder is not for sale – "the player is not transferable," a source said – but any indication that they would consider allowing him to leave would force Fábregas's hand as it would be clear that he is not considered central to the plans of Tito Vilanova, the Barcelona coach. However the news of United's bid came as a surprise to Fábregas, so the player's thoughts are not yet known.

Moyes has turned his attention to the 26-year-old after Thiago Alcântara joined Bayern Munich from Barcelona for £21.6m. Yet it is thought that Moyes could have signed Thiago over the course of the past weeks, with the delay in his finally leaving for Bayern being down to United's manager not being completely convinced by the 22-year-old. Although it is understood Thiago was keen on joining United, there were suggestions from some at the club that he might struggle on occasion to cope with the physicality of the Premier League.

Last month Fábregas said he wanted to stay at Camp Nou. "I've always said that I'm happy at Barça. Whoever says that I'm leaving doesn't know me and has never spoken with me," he said.

"Nor with my agent, because he knows that I don't want him to talk with other people about me. I'm very private and I don't even talk about these things with my family. If someone says anything that isn't that I want to play at Barça, it's completely absurd."