Barcelona coach Luis Enrique has said he wants Pedro to stay in Catalonia and revealed the player has not expressed his desire to leave.
Bournemouth have signed St Etienne striker Max Gradel on a four-year contract for an undisclosed fee.
Berahino, 21, scored both West Brom’s goals in the season-opening 2-2 draw with Sunderland in the Premier League on Saturday.
The England Under-21 striker caught the eye with nine goals last season and he reminded the league of his talents again against the Black Cats.
But Irvine is confident the club would not consider a sale.
Irvine said: "I think everybody should know about him already, but I can't see any way this club would be interested in letting Saido go. You can't let top young English talented players go.
"It could be a very big season for him. He is a terrific lad, he is very talented and he works very hard at his game. He is a pleasure to work with.
"He has got a love for football and with the talent and professional attitude he has got, I think he could be a very good player for this season and beyond."
Irvine himself is under pressure to hit the ground running at The Hawthorns having been the club's surprise choice as new head coach.
The Scot was David Moyes' assistant for five years at Everton but his only previous spells as a manager, at Preston and Sheffield Wednesday, were outside the top flight.
His reign did not start well as Lee Cattermole fired Sunderland ahead with a stunning long-range strike after just five minutes.
Berahino levelled with a penalty after Valentin Roberge was adjudged to have fouled Victor Anichebe despite only minimal contact - even Irvine admitted the decision was "soft".
Berahino added a second after 74 minutes but Sebastian Larsson snatched a point for the Black Cats by rounding off a fine move five minutes from time.
Irvine said: "The first game of the season is always special because you've spent a long time working towards it.
"But it was special for me as well, to do it in the Premier League was something different. The actual occasion was similar to a big game elsewhere."
Record £10million signing Brown Ideye did not get off the bench.
Irvine said of the Nigerian: "He's been with us for a week. He is in good condition physically but I think it would be a big ask for him, physically and in understanding what we need him to do.
"He is still getting to know the names of everyone. It is asking a lot to throw someone into a Premier League game at that point."