The former Gunners center back believes it would be "crazy" to allow the 23-year-old to leave at the end of his contract, and hopes the north London club can convince him to stay
The Gunners’ winger – who has been at the club for almost seven years – is out of contract at the end of the year and has yet to agree a new deal.
But Campbell believes Arsenal would be “crazy” to lose a player on the cusp of his prime years, and has insisted Arsenal must find a compromise that keeps him at the club.
"Theo is a big player," Campbell told BBC Sport. "You don't want to lose him for the best years of his football. For the next five years, I'd pay to keep him. He's a young lad, a good lad who scores goals, and you need to keep those types of players.
"People love him, people hate him - but Theo is a good player, a great player, and he's growing every year. You can't lose him because his contract is running out or he wants a little bit more money. You've got to keep those type of players. We've lost too many over time.
"It used to be losing these players at 30 years old - now they're losing these players at mid-20s and that's crazy. You can't be losing players at mid-20s because of contract situations - it's crazy now."
Gunners boss Arsene Wenger received significant criticism after the Gunners’ Capital One Cup exit to League Two minnows Bradford, but Campbell still backs the French manager.
“He is the right man for the job, but he has to realize that the playing landscape has changed and the market has changed," the former England center back added.
"You've got to sometimes take a risk. Taking a punt on a player 10 years ago for 500,000 pounds might now be seven million. You can't always get these 500,000 pound players, turn them into great players and sell them for 20 million.
"Seven years plus without a trophy for Arsenal is too long. Arsene would be the first to say that. Why not wait until January and just go for it?"