The 21-year-old netted an injury-time penalty in Saturday's 2-2 draw with Crystal Palace to take his goal tally to seven for the season.
Irvine was working as a coach at Everton when Rooney - now Manchester United and England captain - rose through the ranks at the Toffees, and he claims that Berahino has all the qualities to scale similar heights.
"If you are going to be a top player, you have to have a lot of the full package," he told Sky Sports News. "Everyone talks about technical, tactical, physical, psychological. You cannot be a top player unless you score highly in all of them.
"You might score more highly in a couple of areas but you can't possibly be a top player if you don't score highly in all. Saido has a lot of that package but he is still at that age where it can go one way or another.
"The last thing you can do is have anything that affects any of those areas. Of course, the biggest of all is the psychological. I have been fortunate enough to have worked with a number of very talented young players over the years. Wayne Rooney springs to mind."
Berahino, who has been linked with January moves to Tottenham Hotspur and Liverpool, is the highest-scoring Englishman in the Premier League so far this season.