He seems that type of lad where nothing seems to faze him
Simon Grayson
"I think when you can do it on the highest stage at the World Cup, you should be ready," he told Sky Sports.
"It's a big step up - of course it is, playing for a club like Manchester United if that was to happen - but I'm sure he'd take it in his stride as he seems that type of lad where nothing seems to faze him."
The Foxes have no intention of selling the England star and still hope he will sign a new deal at the King Power Stadium.
They will only consider selling Maguire, 25, if he makes it clear to them that he wants to go to Old Trafford - and they will demand a fee of £80m for a player who cost them just £17m from Hull 12 months ago.
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Experienced manager Simon Grayson has had his say on Maguire's rumoured transfer (Image: GETTY)
It means United have made back-up plans with Tottenham's Toby Alderweireld an alternative option.
Grayson added: "Maguire has played a lot more in the last few years, he's slightly younger, but ultimately it'll come down to which one will be available.
"Both Tottenham and Leicester City may not want to sell. One club might want to sell and the other not.
"It's very difficult at this time of the year as lots of people are linked with moves but it needs to take two willing parties to make that happen."