Milan revealed on Twitter on Friday that they had acquired the Spaniard on a temporary basis until the end of the campaign, but there was no such confirmation from the Toffees.
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According to Sky Sports, Everton are furious that the Serie A club claimed the deal had been concluded and maintain that talks are still ongoing.
At the time of writing, neither club had made a public statement on the status of the transfer.
Previously, reports have claimed that Milan’s move for the Barcelona academy graduate had stalled due to the two clubs’ failure to agree a loan fee.
Deulofeu has made just four Premier League starts for Everton this season having fallen out of favour under new manager Ronald Koeman.
He joined the club on a permanent basis in the summer of 2015 after impressing while on loan from Barca during the 2013-14 campaign. In between, he was sent out on loan again by the Catalans to Sevilla.
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Deulofeu was not included on the list of players in Milan’s squad for their crunch league match against Napoli this weekend.
Vincenzo Montella’s side, currently in fifth, will be just a point behind their third-placed rivals with a game in hand if they secure victory at San Siro on Saturday evening.