The Newcastle loanee was a hit at the Hawthorns this season, scoring 24 goals for Albion.
But after failing to win promotion to the Premier League, Gayle's £55,000-a-week wages are too steep for the Baggies, according to the Express & Star.
When Albion technical director Luke Dowling was asked if there was any prospect of Gayle being signed permanently, he said: "No. No-one would like to keep Dwight more than myself.
"We can all recognise what he gives us on the pitch and the way he conducts himself off the pitch in the local area – he's brought his family down from Newcastle for the year, he's bought into everything we want to do.
"Financially, we were prepared to pay the money for Dwight's contract for this season. It hasn't worked out (because we didn't win promotion).
"Dwight's contract is a Premier League contract and we will pay Premier League contracts, but we'll only do that once we're back in the Premier League.
"I know it won't be the news Albion fans want to hear, but they need to trust us and know we're doing everything right for this club.
"We don't want to keep players on big contracts and have to lay the general staff off and make people redundant.
"We want to keep everyone here because we've got good people behind the scenes. But we will still have a competitive wage bill on the pitch next year."