As things stand, the 26-year-old will be up for grabs in the summer, with talks over a new contract at the Emirates having hit the buffers and Wise is of the opinion that the England international would be perfect for the 'Blues'.
"If Chelsea needed a midfield player I would definitely take Jack Wilshere," he told 'The Debate' on 'Sky Sports'.
"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."
Wilshere has been linked with a host of clubs in recent months, including Manchester City, Liverpool, Juventus, AC Milan and most recently Wolves, but Wise believes that he would provide better value for money than some of Chelsea's other recent signings.
"I can't see him going to Wolves. I think he'll get a better club than Wolves," he insisted.
"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."
Finally, Wise played down Wilshere's injury problems, saying that you cannot use them as a stick to beat him with forever.
"He's a bit of a leader, I'm telling you. He gets stuck in, he doesn't mess about and he has got a presence. I like him, I'll have him. Send him down to Chelsea!" he enthused.
"I think he would be a great asset to them, I really do.
"His injury record is what it is. Someone could get injured tomorrow, so that doesn't matter. He has proved he has come back to get away from these injuries.
"How long do you stick that enigma on him? He has proved himself over the last year what he's capable of. He's got himself back to playing top football.
"You think to yourself 'well done Jack.' Everyone was writing him off 18 months ago, but he has shut them all up.
"His timing is spot on. His agent must think they are in a really comfortable position."