Elliott spent two years in the east end of Glasgow and believes the Arsenal defender would be a big hit with the Hoops faithful.
"I know Sol very well and I was talking to him about a month ago. I said to him one thing - if you have the opportunity to go to Celtic, you must take it," said Elliott.
Elliott added: "He's 35, he's played in World Cups, the Champions League and I have to say he was consistently outstanding for Arsenal last season. He has been very injury-free in his career."
Campbell may be in the latter stages of his career but Elliott has no doubts about his ability to make an impact at the Glasgow giants.
He added: "Somebody of that magnitude, if Celtic were fortunate enough to get him, certainly would make a positive contribution.
"He has got a great regard for Celtic, there is no question about that.
"I think, come judgement day, Celtic is not the only option. There are other options to think about.
"He is a very nomadic kind of guy, very comfortable in his skin and I think he would deliver tremendous potential. Certainly, that kind of challenge would be very appealing."