The Irishman played alongside the England striker at Manchester United, and was well aware of his potential from the beginning.
"You were well aware of his potential, just because of the type of attitude he had," O'Shea is quoted as saying by the Sunderland Echo. "He was one of those that when he did come and train with the first-team, he wasn't afraid to try anything. As well as that, he was harassing defenders as well.
"You could see his attitude was going to take him a long way. I know Danny very well and he's made a quick start to life down at Arsenal. Playing in a central role he's flourished. He's been looking to do that for a long time now. But he's the type of lad whose unselfish and is willing to put the work in for the team.
"He did that at United whether he was on the left or the right. But as you'd expect with the type of players Arsenal have, he's getting little combination play and he offers that threat in behind too. We're fully aware of his capabilities."
Welbeck has scored twice for Arsenal in the Premier League since moving from Manchester United.