Barkley became a Chelsea player in January this year for a fee of around £ 15m.
The midfielder initially struggled to break into the team under Antonio Conte as he worked his way back after a lengthy thigh injury.
Since Maurizio Sarri arrived in Chelsea in the summer, Barkley is thriving.
The attacking midfielder has played 15 times in all competitions this season, scoring three goals and earning a place in the England team.
Barkley will face Everton for the first time in his career on Sunday as Marco Silva's team visit Stamford Bridge.
Nicholas believes Barkley would have been successful under Silva, who became Everton's summer head.
But the Sky Sports Pundit says the 24-year-old has performed well since leaving for Chelsea.
"Probably good, I think it would have been an advantage for him," Nicholas continued when Barkley played Silva.
"I think he likes these creative players.
"But the guy has been drifting for a while, he's drifting.
"I was never really convinced that he understood the situation or where he wanted to go.
"I think we were all pretty surprised that he chose Chelsea and if he would join the team.
"It took a long time for a new manager to come in and say," I like your technical skills, but you have to keep going. "
"We talked about it last week – getting more mature, knowing when to come by and when to be aware of it.
"The No. 10 position against teams who do not have much possession is very difficult.
"They try to force everything and make it interesting, if you can, but you have to get the basics right.
"But the lad's career has evolved, he's back in international setup and he's playing very well right now. So the signs are good for him. "