The Hammers were watching Zuber in 2017 when Slaven Bilic was at the helm, but they decided against making a move for the Switzerland international.
Initially, it looked like they may have swerved a bullet as Zuber's form at Hoffenheim fell away. However, his performances on loan at Stuttgart in the second half of 2018-19 have led to renewed interest.
Zuber was struggling with Hoffenheim but boasts five goals and one assist in 13 appearances at Stuttgart and the likes of Nice, Lazio and Roma have all been keeping a close eye on him.
The 27-year-old will enter the final year of his contract with Hoffenheim this summer and reports claim he could be available for a fee in the region of £6million.