The Former Arsenal midfielder has been targeted as a priority for United, who want to strengthen their midfield after losing Paul Scholes to retirement, and with question marks still over the health of Darren Fletcher.
But although Arsenal have first priority on Fabregas if Barcelona want to sell, it appears the Spaniard would want a fresh challenge if he was to return to England.
Fabregas has only scored 10 goals in his 30 league appearances this season, as the Catalan club regained the La Liga title from Real Madrid.
And if Moyes can’t sign the Barcelona midfielder, then he will turn his attention to Real Madrid’s Luka Modric.
Both players have struggled to get regular first team action since they left the Premier League.
Everton midfielder Fellaini has also been linked with a move to United, but it seems Fabregas is Moyes’ priority.
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