Hammers boss Sam Allardyce is also believed to be a big admirer of the 20-year-old, and is willing to swoop for his signature before many of Europe’s elite clubs.
Xhaka is thought to be high on the former Blackburn coach’s list of summer targets, as he looks to add some creative flair to his squad.
Allardyce will face tough competition from Napoli and Lazio, who will, likely, be able to offer the youngster European football.
But, with his chances of regular first-team action liable to be greater at Upton Park, West Ham could have an advantage in the battle.
Reports suggest that Allardyce was monitoring the wide man during January, but decided against making a mid-season move.
Xhaka started his career with FC Basel, where he was one of a crop of talented youngsters.
After almost 50 first-team appearances, the Swiss side allowed him to leave for Monchengladbach in an €8.5m deal.