However, Barkley’s performances have not gone unnoticed, with Chelsea boss Jose Mourinho and Manchester United’s Louis van Gaal reported to be big admirers of the 21-year-old.
It seems unlikely that Martinez is willing to part ways with Barkley following last summer’s transfer ordeal involving the Blues and John Stones.
But Everton favourite Kilbane reckons that Barkley would be a smash hit if he ever swapped Goodison Park for either Stamford Bridge or Old Trafford, although he admits that a move while Martinez is still in charge seems highly improbable.
Kilbane, who made 121 appearances for Everton during a three-year spell, told the Daily Star: “Is Barkley good enough for United or Chelsea? Yes he is.
“I think Roberto Martinez would be quick to stress that he’s going nowhere and he wants to develop him as an Everton player. But he has that [level of] ability. When you watch him play, he can glide past players, he can pick passes out.
"He's taken quite a bit of stick from the Everton fans over the last couple of years. That's because he's a young lad that is going to have inconsistent spells.
"He'll have spells in games where he's not going to be in the match, where you're not going to see him. But this season we're starting to see his skills and his level of performance has been outstanding.
"He's been involved with so many good things. If it's not a direct assist he's played a big part in the lead up to Everton's goals quite a lot this season.
"If you're talking about playing for one of the top sides of course he has that ability. He's got power, he's got pace, he's two footed. He has that rare ability to change a game and bring it to life."