Under similar circumstances, West Brom's opponents on Monday, Everton, managed to keep hold of defender John Stones, who also had a transfer request rejected, after being heavily linked with a move to champions Chelsea.
With the league's jaw-dropping 5.14 billion pounds ($7.80 billion) domestic TV rights deal set to kick in from next season, Pulis felt clubs will keep their key players unless the price is right.
"I think the stakes are so high now for every club in terms of keeping Premier League football, that unless it's right it won't happen," Pulis was quoted as saying by the British media.
"If it's right then everybody has got a value. I just think the value of people and what's going on has changed.
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"You would have thought that Tottenham would have got Saido at a certain price and you would have thought Chelsea would have got Stones at a certain price so it was nice that it didn't happen, for everybody."
The former Stoke City manager also said the transfer fees being paid for players are ridiculous, but expects the value of players to increase.
"In my opinion the transfer fees 10 years ago were ridiculous so don't even ask me what I think of them now," Pulis said.
"The top clubs want the best players, they will spend to get the best players and the market value will keep going up because the money is getting bigger and bigger, especially in the Premier League."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
