The Baggies confirmed on Monday that they had turned down a transfer request from the 22-year-old striker.
Berahino, who scored 20 goals last season, has been heavily linked with a move to Tottenham Hotspur.
Despite speculation concerning his future with West Brom, Irvine believes that the youngster will develop into a better player if he remains at The Hawthorns.
"If I was asked for my opinion by Saido, I would say to him, 'stay where you are'," the Scottish coach told talkSPORT.
"From Saido's point of view he feels it might be the right time and the right club to move to, but personally I think young players who are still developing, as Saido is, should be at a club where they can continue that development.
"He's got a lot of potential, he's got good movement for a young player and finishes well with both feet, but there are things that he still needs to develop and improve and I think he'll be given a chance to do that at West Brom."
West Brom are in action tonight when they host Port Vale in the second round of the League Cup.