Barkley, who is one of the most talented young players in Europe, has been included in the 23-man England squad for the Euro 2016 finals in France this summer.
The 22-year-old is not likely to start matches for the Three Lions, but he will play his role from the substitutes’ bench.
Former United midfielder Robson has suggested that Barkley could do something special at the Euro 2016 finals in France.
The former England international star has also compared the Everton attacking midfielder to Paul Gascoigne.
Gascoigne is one of the greatest players in English football history, and featured for the likes of Newcastle United, Tottenham Hotspur, Rangers and Everton.
“Then we have Barkley who, like Wilshere, can provide something special,” Robson told The Sun. “And I think a competition like this could just make him — he could become our new Gazza.
“Just like Gascoigne, he has got so much instinctive ability. He’s got quick feet, can ghost past people and has good vision.”
Barkley scored eight goals and created 55 chances in 38 Premier League appearances for Everton this past season.
The England international attacking midfielder had a pass accuracy of 86% and a shot accuracy of 51%, and won 27 headers, 115 dribbles and 23 tackles.