The Sunderland striker will be available, reportedly on a free transfer, after the Black Cats were relegated from the Premier League last weekend
Pulis has gone through the majority of the season with just Hal Robson-Kanu and Salomon Rondon as available strikers with Saido Berahino barely playing, due to a two-month ban for failing an out-of-competition drugs test, before he joined Stoke in January
Defoe, 34, has scored 14 of Sunderland's 26 goals in the Premier League this season and boss David Moyes has confirmed the England international has an escape clause in his contract, with West Brom considering a move
"When you say he's a free agent, effectively he's a free agent, but that still brings an enormous cost to whichever club takes Jermain," said Pulis, ahead of Saturday's trip to Burnley
"We've got our fingers in the pie on quite a few players and we'll see how we go on those players
If Jermain's one of them, we'll be pushing on that one if we can
"When Saido left we had Robson-Kanu and Salomon, a free transfer and a player that's only spent one season in the Premier League, so we knew that was an area we had to improve.
"There was no-one there at the time that we could get in
And I don't want to waste people's money by spending a lot of money on just a back-up
We have to try and bring players in who are going to improve the first XI and keep the club improving that way.
"That's the way I've always thought about it, that's the way I try to approach it
That will certainly be one of the areas we're trying to improve."
The Baggies are also interested in Leeds left-back Charlie Taylor and are in contract talks with defender Craig Dawson
"He's been offered a contract, again I'm not getting too involved in it," Pulis added
" I'm not sure how far they are but from what I can gather Craig wants to sign and the club want him to sign."
Meanwhile, Matt Phillips and Robson-Kanu (both hamstring) are out of the game at Turf Moor with Albion looking to end a run of five games, which has included four defeats, without scoring
Pulis added: "We might make a few changes, freshen things up and see how we go."
Source : PA