According to Sky Sports News, Rojo was at Manchester United's Carrington training ground earlier to discuss an exit.
United's acquisition of Harry Maguire from Leicester City for £85 million has pushed Rojo further down the pecking order at Old Trafford.
Everton are keen to sign a central defender following the news that last year's loanee Kurt Zouma will be staying at Chelsea at Frank Lampard's request.
The Argentine is thought to be looking for regular first-team football, and Everton are reportedly willing to offer him that.
Rojo has two years left on his current Manchester United contract, with an optional third that can be activated.
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