Former skipper Wile led the team throughout their glory heydays of 1970s and in terms of playing style Olsson is as close to anything seen at The Hawthorns since Wile was partnering Alistair Robertson in Ron Atkinson's side.
Wile told the Birmingham Mail: "He has served Albion well. I think the thought process of players has changed now. No-one would ever stop at a club as long as I stopped, or Ally Robertson or Tony Brown. It just wouldn't happen today for several reasons.
"People tend now to follow pound signs, to be honest. There's nothing wrong with that because it is a very short career and you're very soon forgotten.
"I've got no reason to say he's doing the wrong thing. If he can find himself a better contract and subsequently make his life more secure, then he has to do what he has to do.
"If he can do that at the Albion, that's all well and good. If he has to go elsewhere, then he has to go elsewhere."