The Luzern midfielder has been turning heads this season with his performances in the Swiss top tier, where his side sit in fifth.
He broke into the Switzerland squad last year and has earned two caps for his country already.
The 21-year-old was heavily linked with a move to Italy last summer but he stayed put at the Swiss outfit.
According to Italian sports daily Corriere dello Sport, Jashari is one of the names West Ham are interested in.
The Hammers are still looking at potential midfield recruits despite signing Edson Alvarez and James Ward-Prowse in the last summer transfer window.
Jashari is being closely courted by West Ham on the basis of reports on him from their recruitment team.
The east London club are facing competition from Spain as Villarreal are also interested in the Swiss international.
West Ham have prioritised signing a striker in January but it remains to be seen whether they have money available to sign Jashari in the winter window.