Pulis and Baggies chairman Jeremy Peace have both previously intimated they had no interest in selling the 14-goal striker, who is being monitored by Liverpool.
Peace did, however, add in a statement this week that the final decision lay with Pulis, who has now conceded a mammoth bid for the £25million-plus rated 19-year-old could yet force their hand.
Pulis said: "The problem with talking about any players at this time of the year is that if someone comes in with an unbelievable offer you can't turn down then you have egg on your face.
Saido Berahino Player Profile
To say he's not going anywhere, that's difficult at times, you never know what's around the corner
Tony Pulis
"To say he's not going anywhere, that's difficult at times, you never know what's around the corner. That's why the chairman said it would be the manager's decision in the end.
"I'd have to decide and take into account what we've brought in and what we've been left with. Staying in the Premier League is vital. What's it worth next year? Hundreds of millions.
"We've not been offered any money yet. But you'd have to sit down and think about it - and you'd have to look at how strong the squad was he was leaving to agree to it.
Pulis has confirmed he has held talks with Darren Fletcher - but is in danger of missing out to West Ham for the Manchester United midfielder.
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