The talented right-back, 23, has been linked with a host of top flight English clubs, with Manchester United reported to be at the head of the queue to secure his services.
Having spent eight years in the Premiership himself with Everton, Weir has little doubt that Hutton has the ability to play at that level.
But the veteran centre-half believes there is plenty of time for Hutton to demonstrate just how far he can go in the game.
"He's a great player, there is no getting away from that," said Weir.
"From the moment I came here I've been very impressed by him. Obviously people will take notice of that, it's the nature of the game.
"But I don't think Alan is in any rush to leave and I think he enjoys it here. It's a great club to be at and a great place to play your football.
"He's a young man and he has his future ahead of him. I'm sure his career will map out the way he plans it."
And, although £8million has been touted as the asking price for the highly-rated full-back, Weir believes Rangers would be unwilling to part with their prize asset just yet.
He added: "I can't imagine Rangers are in a rush to sell their best players, I don't think that's conducive to winning the league which is everybody's goal. Time will tell on that one."