The 21-year-old netted his eighth goal of the season on Saturday, as his stoppage-time penalty rescued a 2-2 draw against Crystal Palace at The Hawthorns.
When asked if he felt that the England Under-21 international could become an elite player, Irvine told the Express & Star: "I think so. As long as he goes about his job in a way he is doing now – on the field and off it.
"As long as he keeps having this desire to improve which he has at this moment. Then of course as long as he can handle the pressure of success.
"Some can't handle that pressure, they get distracted so it is important he takes everything that is going on at the moment in his stride. I have quite a lot of chats with Saido – nothing major, just little chats to just make sure he is going down the right road."
Reports have suggested that Liverpool are preparing a £25m bid for Berahino in January.