Xhaka, whose younger brother Granit plays for the Hammers' London rivals Arsenal, could be on the move next month and would reportedly cost £4 million.
West Ham have been linked with a number of players in Xhaka's position - including Serbian pair Nemanja Maksimovic and Luka Milivojevic - ahead of the winter transfer window and are said to be considering an approach for the Albania international.
Arsenal's Granit Xhaka (left) is tackled by Basel's Taulant Xhaka
However, it is claimed that Spanish giants Valencia are also 'watching developments'.
Xhaka, 25, is a more defensive-minded midfielder than his brother and can also play at centre-back if required.
The pair famously played against one another at this summer's Euros, with Granit's Switzerland emerging as 1-0 winners against Taulant's Albania in the group stage, and again at club level this season.
The pair swap shirts after this month's clash in Switzerland
Despite also losing both Champions League encounters against Arsenal, Xhaka and has tasted defeat in just one of his 17 domestic outings this term.
Would Xhaka be a good signing for West Ham United?
Have something to tell us about this article?