Schlupp celebrates pre-season goal with new boy Ahmed Musa
The Baggies are said to have had a £9 million offer turned down for Schlupp, who is being lined up to fix Tony Pulis' problem left-back position.
Pulis is short of natural left-back options
Wingers Chris Brunt and James McClean were often forced to play out of position last season, along with centre-backs Jonny Evans and James Chester.
Leeds' Taylor has a year left on his contract
According to the Sun, the Baggies will offer an extra £1 million for the versatile Ghanaian, who can also play as a winger and began his career up front.
Schlupp made 24 appearances last season, en route to the Premier League title, and was directly involved in four of the Foxes' 68 league goals.
Schlupp attempts to tackle Everton's Kevin Mirallas
However, only 14 of those outings came as a starter, and the Hamburg-native is likely to play second fiddle to Christian Fuchs again this coming campaign.