HITC Sport understands Leeds rejected bid from West Ham for defender.
Taylor's future at Leeds has been the subject of intense speculation for some time with the player into the final year of his contract at Elland Road and no sign of an extension being agreed.
The 22-year-old handed in a transfer request last week which was immediately rejected by Leeds with the club adamant the left-back will not be sold this summer.
West Ham have been keeping tabs on Taylor's situation at Leeds and they are understood to have firmed up their interest with a £7million bid last week as they looked to bring in cover for the injured Aaron Cresswell.
However, Leeds turned down the offer for Taylor and the defender started Sunday's opening game of the new EFL Championship against Queens Park Rangers.
West Ham have since brought in French left-back Arthur Masuaku from Olympiakos and it remains to be seen if that will end their interest in Taylor.
Leeds now run the risk of losing Taylor for free next summer if he runs down his contract and if he stays at Elland Road when the transfer window closes there is sure to be more speculation about his future in the winter transfer window.