McAvennie makes 'biggest in the world' claim amid update on Rangers swoop for McBurnie
The Leeds-born Scot, 25, signed for Sheffield United in the summer of 2019 for a reported £20million fee.
He was signed after a prolific Championship season with Swansea as he bagged 22 goals in 42 outings.
He only scored once in the Premier League during the recently concluded season despite making 23 appearances.
McAvennie claims Rangers already have enough strikers after recently signing Fashion Sakala from KV Oostende.
“Sheffield United are going to want a decent fee for him,” McAvennie told Football Insider correspondent Ben Wild.
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“Rangers don’t have that kind of money. Not for a striker who doesn’t score goals.
“They have a lot of strikers already as well, I know they have signed that lad from Belgium [Sakala].
“Maybe he’s [McBurnie] not been able to live up to that price tag but Glasgow is the biggest goldfish bowl in the world.
“Trust me, it is, I’m not sure that would do him any good. He’ll have no freedom up here.
“He’s got something, just hasn’t shown it. I would be very surprised if Rangers sign him, especially for that money.”
McBurnie has only scored seven goals across two seasons at Bramall Lane.
Sheffield United were relegated from the Premier League after only picking up 23 points across 38 games last season.