The former Arsenal man believes Ronald Koeman could get the best out of him.
The midfielder had his best season in terms of goals and assists last year, despite his side struggling and finishing 11th in the table.
He headed to Euro 2016 with England, but alongside Everton teammate John Stones, failed to be given a single minute of football at the tournament.
Everton manager Ronaldo Koeman
He is now working with the Blues in pre-season under new manager Ronald Koeman, looking lively in their two friendly wins so far.
And Parlour believes he is set to play a major part for them next season as Koeman may be the man to get the best out of him.
“Ross Barkley looks like he will be staying and he’s going to play a major part,” he told talkSPORT.
“I think Ronald Koeman might be able to get the best out of him. They’ve got a good manager there.”
Everton's Tom Davies and Ross Barkley in action with MK Dons' Samir Carruthers
It will certainly be interesting to see if Barkley can play a major role under Ronald Koeman next season.
Roberto Martinez was key to his development, but the Spaniard appeared to be struggling to help him keep progressing towards the end of his reign.
Koeman is likely to have his own plans for him though and Everton fans will be hoping that Parlour’s prediction comes true.
Everton manager Ronald Koeman before the match against Barnsley