The Foxes striker emerged as a shock target for Arsenal on Friday when they activated a £20million release clause in his current contract.
A conclusion to the deal had been expected on Monday, when it was reported that Vardy would inform Arsenal manager Arsene Wenger whether he would be joining or not.
However, he failed to get in touch, with the Frenchman said to fear that the England man will turn down a move to the Emirates Stadium.
Smith though has urged him to make the switch as this kind of opportunity may not come again for him.
“It was always going to happen, the bigger clubs are always going to try and cherry pick the Leicester players,” he told talkSPORT.
“It is a big move for him but my advice would be that I think he should grab it. The chances are that this kind of opportunity won’t come again.”
It is easy to see why Vardy will want to take his time before deciding on a move to Arsenal.
He has enjoyed tremendous success with Leicester and fits perfectly into the style they employ, something that has helped make him become such a big success.
An offer to move to one of the traditional big clubs should not be turned down quickly though, and it will be fascinating to see which one he ultimately chooses.