The 29-year-old, who has 12 months left on his contract, has attracted interest from a number of clubs.
But it has been reported that Wanderers have accepted a bid worth an initial £2.2million from the Hammers.
Taylor was signed from Portsmouth for £3.5million by Gary Megson in January 2008 and with only a year left on his deal Bolton are happy to let the midfielder leave.
He failed to reproduce his best form last season, scoring just twice, and found his left-sided position under threat from Martin Petrov.
Taylor was an unused substitute in Bolton's second friendly of their US trip, a 3-1 win over Orlando.
The player must now pass a medical and agree personal terms with West Ham, where he will join up with former Wanderers captain Kevin Nolan.
Taylor's departure and the subsequent income it generates should help spark some transfer activity at the club with manager Owen Coyle interested in Barcelona forward Jeffren and former Aston Villa midfielder Nigel Reo-Coker.