A six-over 78 saw him drop down the leaderboard to such an extent he did not even win the Silver Medal for top amateur but after September’s Walker Cup, Dunne will make the step up to professional.

“Certainly once the Walker Cup is over – whether he’s selected or not, he’s certainly going to have a go at turning professional,” father Colum told RTE.

McDowell, the 2012 US Open winner who coincidentally attended the same University of Alabama as Dunne, believes the golfer from Greystones south of Dublin has proved he can cope with the additional pressure and demands.

McDowell said: “I played with him early in the week and he hit the ball very well with a technically-correct swing.

“Listening to a few of his press conferences he seems like a wise-old owl for someone his age.

“He seems like a really cool character. I liked his comments about being surprised to be leading an Open Championship but not surprised about the numbers he shot.

“He has that Jordan (Spieth) maturity to him a little bit.”

The Ryder Cup star believes had Dunne maintained his progress and finished strongly in the final round he should have turned pro immediately but admits the Walker Cup is also a special event to be involved in.

“If he had a good finish I don’t know what he would have needed to have waited for the Walker Cup for,” he added.

“The Walker Cup is one of the fondest memories of my career but it means nothing as soon as you press the professional button.

“He needs starts and has an opportunity between now and the end of the season to perhaps get his European Tour card and those extra five weeks could be beneficial to him.

“It is a tough call and I’m not the guy to advise him.”

Dunne was one of five amateurs to make the cut at St Andrews and there was intense competition for the Silver Medal, won by American Jordan Niebrugge.

“When you see three amateurs within three or four shots of the lead it says how good they are,” said McDowell.

“It is a belief and acceptance level of competing at the top level as a youngster – 19, 20, 21 years old.

“There is a readiness that is there what wasn’t there when I was turning pro.

“I am probably a bad example as I had never been to a professional tournament until I played in one (as a professional).

“Tiger (Woods) and subsequently Rory (McIlroy) and Jordan (Spieth) have raised the bar to say you don’t have to be a late 20s- early 30s mature veteran to be able to compete in the top tournaments – the WGCs (World Golf Championships), majors – you can do it right this second.”