The Belgian met with Toffees boss Roberto Martinez at the club’s Finch Farm training base on Monday evening before leaving shortly before 8pm, with United looking to complete a deal before the 11pm deadline.
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The Belgian FA confirmed earlier on Monday that the midfielder had been given permission to delay meeting with his national team squad in Neerpede ahead of their clash with Scotland on Friday, with a view to allowing him more time to complete a move to Old Trafford.
A move for Toffees left-back Leighton Baines, however, is looking unlikely; Everton are reluctant to sell the England international while, unlike Fellaini, Baines is not expected to hand in a transfer request to force through a move.
United boss David Moyes is also keen on securing a move for Athletic Bilbao midfielder Ander Herrera although it remains to be seen if Old Trafford officials can push through a deal before the transfer window closes.
Everton, meanwhile, have made an approach for Cagliari defender Davide Astori while the club are also chasing deals for Manchester City duo Gareth Barry and Joleon Lescott, as well as Wigan Athletic midfielder James McCarthy.