Barry was overlooked for England’s latest squad by manager Roy Hodgson, despite his fantastic form for the Toffees this season.
Roberto Martinez had called on Hodgson to recall the 33-year-old, after admitting he was impressed with his skills and leadership abilities.
But Hodgson’s snub has it looking likely Barry has played his last game in an England shirt, but that has not put Everton off wanting to make his loan signing permanent.
The Toffees are ready to offer Barry a deal that would see him playing at Goodison Park until the age of 36, reportedly worth £50k a week.
Two of the years will be guaranteed, with a third to be offered if the former Aston Villa captain plays enough games.
Barry will become a free agent in the summer when his contract at Manchester City expires.
He has previously been linked with Arsenal, but he is unlikely to find better terms than what Everton are preparing to offer.
Barry is also settled at Goodison Park, and would be almost guaranteed regular first team football.