The 17-year-old, who has been with Everton since the age of 11, has impressed in pre-season and is likely to get his chance in the first team.
Striker Saha said: "I think he's got all the ability to be a great player for Everton and for England. Hopefully he will show that this season.
"It's not too early for him because he's got all the attributes to surprise a few people. He's got power, strength, confidence, speed - he's said a few times to me that I'm slower than him. Hopefully he will show that to the Premier League this season.
"I'm enjoying training with him and hopefully I will enjoy playing with him because I think he's got so many talents and he will definitely be a big star if he keeps working hard."
Barkley, a tough-tackling midfielder with an eye for goal, looked set to break into the first team last season but suffered a horrific broken leg on England Under-19 duty that cut short his campaign.
His talents were also espoused by defender Sylvain Distin, but the Frenchman is hoping Barkley will not have too much pressure placed on his shoulders.
Distin said: "He seems to be an amazing player but the problem is after one or two games people put too much expectation on the young players. I want to give him time. But definitely he's got quality."
As well as Barkley, 21-year-old striker Magaye Gueye and 18-year-old Conor McAleny have also impressed in pre-season, and Distin believes their rise can provide some much-needed depth to the squad.
He added: "It's a good thing, especially because we seem to have quite a few injuries through a season so you need those kind of players to be there and push the old players like me to train harder and be even better."
Meanwhile, Everton captain Phil Neville has backed Seamus Coleman to come back stronger after it was confirmed yesterday the Republic of Ireland international tore a ligament in his right ankle in the friendly defeat by Villarreal last Friday.
"Everyone knows what I think of Seamus, he's a fantastic character and a great person to have around the place," Neville told evertontv.
"With the attitude he has, he'll have no problems coming back fully fit. He's a real warrior and someone you'd like to go to war with. I'll personally miss him and I know the team will."
Everton are still waiting to find out whether Saturday's Premier League opener against Tottenham at White Hart Lane will go ahead following riots in London and other cities.
Neville added: "Other things are slightly (over)shadowing events at the moment and quelling our enthusiasm, but we can't let these people win. Hopefully the game will go ahead on Saturday and we're all looking forward to the season."