Pulis has been a long-term admirer of the 23-year-old, who is a free agent this summer when his contract at Leeds United expires.
And the Baggies reportedly started speaking with his representatives when it was confirmed Garry Monk's team had all-but missed out on the play-offs.
But because Taylor is under 24 and has risen through the youth ranks at Elland Road, Albion may be forced to pay United a substantial fee by the Professional Football Compensation Committee.
Taylor is not the only left-back on Albion's radar and Pulis confirmed he was looking at other options.
“Charlie is one of the players we’re looking at in respect of left-backs but he’s not the only one," said Pulis. “He’s a possibility. The problem with that one is it would go to a tribunal so we’re not exactly sure what the fee would be.
“We don't know the costs on that one. That would be a difficult one but he’s one we have talked about. He wouldn’t be a free transfer."
Liverpool were ordered to pay Burnley £6.5million in compensation potentially rising to £8m when they snapped up striker Danny Ings on a free.
Leeds have rejected offers of £7m for Taylor from several Premier League clubs in the past, which suggests the Baggies may need to stump up a similar amount at tribunal.
But Taylor is exactly the right age of player Pulis is targeting this summer and Albion desperately need a left-back, having played Allan Nyom and Chris Brunt out of position in that role all season.
“We’ve got the oldest squad in the Premier League,” said Pulis. “Having said that I think we’re in the top three in respect of output fitness wise. The lads will have a little bit of a go at me if I say the group is too old.
“But it’s just under the mid 20s we need players. We’ve got some good young players but we need to find that middle ground as well.
“I think the balance of the squad is most probably tipped at the top end, and we’ve got to find that middle ground a bit.”