The former Arsenal captain is available from Bayer this summer and has been interesting AC Milan.
La Gazzetta dello Sport says Juve are also keen, particularly if they can find a buyer for Douglas Luiz.
Juve coach Igor Tudor is a fan of Xhaka and would view him as a midfield first-choice should he arrive.
Xhaka, 32, is available from Bayer for €10-15m.