Taylor, who courted controversy by refusing to play in Leeds' final game of this season, has been given a month to respond to the offer.
Baggies boss Tony Pulis does not want to take the risk of going to a tribunal for the 23-year-old left-back, who is out of contract at Elland Road this summer.
Pulis has stated that he is not willing to risk having to overpay for the Leeds defender and as such there will be no move for him if a fee between the clubs can not be reached.
Leeds United have revealed on their official website that they have offered a new deal to contract rebel Charlie Taylor.
The Leeds player of the season in 2015-16 is understood to have been fined two weeks' wages for his refusal to play at Wigan.
Bud Capitalizes on Jeter Ceremony This Weekend With 'This Bud's for 2'
And I say this very humbly, there isn't a person or player I would trade places with that's playing now or ever . Derek Jeter is introduced as the New York Yankees honor the 1996 World Series team at Yankee Stadium.
"A tribunal could put an extraordinary amount of money on it and you're stuck with it".
It was reported the Premier League had offered £3.5million for Taylor but it was said to have fallen short of Leeds' valuation of the player. "It's a risk that, at this moment, is not worth taking", Pulis told BBC Sport.
New one-year deals have been offered to Eoghan Stokes and Tom Pearce and option have been taken up on the contracts of Conor Shaughnessy and Romario Vieira. "In line with EFL regulations, he now has one month from [Wednesday's] date to accept".
Winger Pablo Hernandez, 32, has had his contract extended by a year after 38 appearances last term.
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