But, according to Richard Dunne, the 23-year-old should reject the terms on offer and seek a fresh challenge to boost his career.
Dunne, who started his Premier League career at Goodison Park, told talkSPORT: "There are a few players at Everton that have gone into their comfort zone and maybe a change would be the best for both sides.
"Certainly for Everton they need a bit more freshness in their team and maybe Ross does, in terms of getting a new club, having to earn a place in a team and not have the comforts of being at home and living in his hometown.
"Maybe he needs to go out and challenge himself and start trying to progress and get a place back in the England team."
Barkley is likely to be in demand should he decide to quit Everton, who reportedly value the talented playmaker at £50million.
Arsenal, Manchester City and Tottenham have all been linked with the England international in recent seasons.
Dunne doubts whether another of his old clubs, City, will follow up their interest but feels a move to either north London club could benefit Barkley.
"Maybe an Arsenal or Tottenham will be better for him [than City]," said the Irishman.
"I think Manchester City will try and sign stronger and maybe better players – players who have won things over the years.
"Barkley is certainly going to move to a big club but I don't think it will be City. I don’t imagine he will get the games he needs."
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