Barkley joined Chelsea last Friday from Everton for a fee of £15million.
The 24-year-old, who has yet to play this season due to an injury, trained with his new team-mates for the first time on Tuesday.
While it remains to be seen when he will make his competitive debut for Chelsea, former Blues star-turned-pundit Wise thinks Barkley could be priceless for the west London outfit.
And Wise thinks Barkley’s versatility means he could play anywhere in midfield.
When asked about the Barkley deal, Wise told Sky Sports’ The Debate: “Ross [Barkley] is a fantastic buy – he’s a talent, not fulfilled what he’s capable of.
“With Antonio getting hold of him, he can be a really good buy.
“He’s a bargain at £15m, and with his talent, he could be worth a lot more.
“I’m intrigued to see where he will play as he wants to score goals.
“Is he going to play alongside Kante or in a wider role – I’m intrigued to see where he starts his first game.
“If you can get him disciplined and get him to break, then he has a talent to open things up.”
Meanwhile, Chelsea were held to a goalless draw in the first leg of their Carabao Cup semi-final tie against Arsenal last night at Stamford Bridge.