Barkley became a Chelsea player in January this year, joining for a fee of around £15million.
The midfielder initially struggled to break into the team under Antonio Conte as he worked his way back from a long-term hamstring injury.
However, since Maurizio Sarri arrived at Chelsea in the summer, Barkley has flourished.
The attacking midfielder has played 15 times in all competitions this season, scoring three goals, and has earned a place back in the England squad.
Barkley goes up against Everton for the first time in his career on Sunday when Marco Silva’s side visit Stamford Bridge.
Nicholas reckons Barkley would have been successful under Silva, who became Everton boss in the summer.
But the Sky Sports pundit says the 24-year-old is progressing well since leaving for Chelsea.
“Probably well, I think it would have been a benefit for him,” Nicholas said on if Barkley played under Silva.
“I think he likes those creative players.
“But the lad had been drifting for a while, he’s been drifting along.
“I never really felt convinced he was understanding the situation or where he was going.
“I think we were all quite surprised that he picked Chelsea and if he was going to get in the team.
“It’s taken quite a bit of time and for a new manager to come in and say ‘I like your technical ability but you’ve got to move on’.
“We were touching on it last week – maturing, being wiser about when to pass, when to be aware.
“That No 10 position playing against teams that don’t get a lot of possession is very difficult.
“You’re trying to force and make everything interesting when you can, but you’ve got to do the basics right.
“But the lad’s career has moved on, he’s back in the international setup and he’s playing very well at the moment. So the signs are good for him.”