"Robbie has for most of his career played at Anfield where there is an expectation among the fans to win every game, home and away.
"It would be the same for him at Ibrox. Rangers is a massive institution. In fact, I can't see him getting the same level of intensity anywhere else.
"Robbie is an unbelievable talent who has enjoyed an incredibly successful career in football. But he needs the same sort of stimulus he has always had.
"If he were to drop down a level to a lesser club, without the same level of pressure on him every week, then I would wonder how it would affect him."
McAllister added: "It is well known that he is an ardent Rangers fan. Over the years he has been up to watch Old Firm matches and other games.
"Fans at all clubs really take to anybody they know supports as well as plays for their team. There would be a nice affinity between Robbie and the Rangers fans because of that."