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 Toffees tried to sign Rojo last summer, but the deal collapsed at the eleventh hour.
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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