With Newcastle United reportedly the front-runners for his signature, the Baggies manager says the decision over the striker's future rests with Jeremy Peace
Berahino threatened to go on strike in September after West Brom rejected a deadline-day approach from Tottenham.
That situation was quickly resolved, but Berahino has endured a difficult campaign - scoring three goals in just eight Premier League starts - and has been heavily linked with a move away from the Hawthorns in the January transfer window.
Tottenham have again been credited with an interest, as have Stoke City, Chelsea and Leicester City. However, it is Newcastle United that appear to have emerged as the favourites to sign him, as they are said to be willing to pay €18 million to land him.
However, the manager maintains the decision over a transfer is not his, but lies with those above him.
"The valuation will be determined by the chairman," he said.
"The chairman will decide whether Saido goes or stays. The chairman will make decisions, financially.
"As much as it's the player, it's the financial deal and like I say, we'll leave it with Jeremy to sort it."
Berahino did not feature during West Brom's 1-0 win over Bristol City in Tuesday's FA Cup third round replay, but Pulis insisted his absence was due to illness rather than because of an impending transfer.
"If he hadn't been ill, he'd have been playing," Pulis said. "He's not been well, he's picked up a bug the same as Lambert and a few of the other lads over the past few weeks.
"We want to keep Saido if we can."