West Ham and West Bromwich Albion are chasing the young Scot.
McAvennie told the Scottish Sun: "Naisy would be a great player for West Ham. It would be a match made in heaven.
"It would be a great loss for Rangers, that's for sure, but it would be a fantastic signing for West Ham.
"He's a player I rate highly and I wouldn't say that about a lot of players. I'd be delighted if he rolled up at Upton Park because he's the type of player the crowd would like down there.
"He's got that never-say-die attitude and he always chases lost causes. But he has ability too and he scores goals."