The Hammers are in desperate need of additional firepower up front, with Michail Antonio currently the club's only recognised centre-forward following the departure of Sebastien Haller to Ajax in January.
Manager David Moyes has money to spend on a new forward, which 90min understands to be around the £30m mark, although there's scope for the money to be invested elsewhere if West Ham are able to agree a loan deal with Monchengladbach.
24-year-old Embolo was relatively goal shy in the Bundesliga last season, netting just five times for Monchengladbach, and that's opened up the possibility of a temporary move away.
Embolo did put in an impressive showing for Switzerland at Euro 2020, scoring his country's opening goal of the tournament during the 1-1 group stage draw with Wales, before continuing to impress as they qualified for the round of 16.