Stirling, 22, has been touted as a possible England player in the future - and follow the path of Morgan in making the switch across the Irish Sea - and he underlined his growing status in Thursday's tied first RSA Insurance one-day international in Dublin, when he hit his second century in as many games against Pakistan.
"Without a shadow of a doubt that kid will go down in history as Ireland's best batsman," said Johnston.
"He's one of the cleanest strikers of a cricket ball that I have ever seen, be it to play with, against or watch on TV. It's just phenomenal.
"I'd probably like to see him use his head every now and then instead of going for some of those careless shots.
"But when he reins it in and plays cricket shots there is nothing better.
"He loves playing Pakistan in Ireland - that's two hundreds. I don't know why he's not playing more cricket for Middlesex.
"They must have some players there because that kid is a freak.
"He should go out and play that type of cricket every time he goes out to the crease.
"That's what is going to bring crowds back to cricket around the world - blokes like him hitting the ball."
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