Wilshere is due to leave the Emirates Stadium as a free agent at the end of next month after being offered reduced terms by the Gunners.
Chelsea have spent a combined £50m to bring in Danny Drinkwater and Ross Barkley over the past year, but Wise believes that another Englishman in Wilshere - linked with Wolverhampton Wanderers earlier this week - would be a far better option ahead of next season.
"If Chelsea needed a midfield player I would definitely take Jack Wilshere," he told Sky Sports News. "He's free, he's 26-years-old and he's proved he's come back to full fitness.
"You see the money they've paid for Danny Drinkwater and Tiemoue Bakayoko and I think he's better than them. I'm sure Arsenal fans wouldn't like me saying this, but he's for nothing if he's walking away.
"Go and have a go at him. Go and take him. I can't see him going to Wolves. I think he'll get a better club than Wolves. At 23, what would you have paid for him? £40m? Would I play him in the Chelsea team now? Yes, I would. I'd sit him alongside N'Golo Kante and I'd play him."
Liverpool and Everton are also reportedly keeping a close eye on developments with regards to Wilshere's future.