The 21-year-old is expected to be named in Roy Hodgson's 23-man party to board the plane to Poland and Ukraine for next month's extravaganza in Eastern Europe.
Welbeck has won just four senior caps to date, but could be set to lead the line in England's opening two group games against France and Sweden, with Wayne Rooney suspended and Darren Bent recovering from ankle ligament damage.
But despite his inexperience at full international level, Robson, who won 90 England caps and participated at four major tournaments, is confident the youngster would not anyone down.
"He’s a real hard worker [and] he’s worked very hard over the last couple of years to develop his talent. He’s just started to score goals now and that will give him great confidence," Robson told Yahoo!
"The way Danny is playing for Manchester United at the moment, he wouldn’t let England down if Roy Hodgson does put him in the squad and ask Danny to fill in for Wayne at this moment in time."
Welbeck's Old Trafford team-mate Paul Scholes continues to be linked with a return to the international fold ahead of the upcoming championships.
The 37-year-old hung up his boots 12 months ago only to perform a U-turn in January having realised he had a mistake in retiring too soon, and went on to 21 appearances in the second half of last season, scoring four times as United narrowly missed out on their 20th league title.
Scholes retired from international duty after the 2004 European Championships, and turned down Fabio Capello's advances two years ago after the former England manager attempted to lure the veteran pass-master to South Africa at the eleventh hour.
However, the appointment of Scholes' friend and former United and England team-mate Gary Neville to Hodgson's coaching staff has led to reports that the midfielder could be tempted to return with the national side still missing his passing prowess.
And Robson believes Scholes is still one of the most talented players in the country in his position and would be a real asset to the national setup.
"I don’t know what Paul Scholes has got in his mind. He retired years ago. I don’t think it’s something which Scholes would probably take onboard after so many years out but there is only Paul who can answer that question," he said.
"He’s probably the most talented in terms of vision and passing the ball. Scholes has got great vision."
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