Campbell, who is coming off contract, has confirmed he's in talks with the Hoops.
And Redknapp told the Scottish Sun: "I said last year, when he joined Notts County on a free transfer, that I couldn't believe Premier League clubs hadn't gone for him.
"As far as I was concerned Sol was easily still someone who could've done a brilliant job in the Premier League.
"Having seen him back at Arsenal last season my opinion was vindicated.
"To be honest, I would be surprised if he didn't stay with Arsenal.
"He'd make sure Celtic were head and shoulders above everyone else."