The Hammers are in the market for a striker after they sold Sebastien Haller to Ajax earlier this month for a fee of €25m.
The 23-year-old En-Nesyri has emerged as one of their targets and the east London club even tabled the first bid, worth €30m, which included €5m in add-ons.
Sevilla turned down the proposal, but it has been suggested in Spain that West Ham are preparing to return with a new offer which could come close to €40m.
But according to Eurosport France, the Hammers will not be making a second offer for the Moroccan striker at the moment.
The Premier League club have paused their attempts to bring in a striker and a second bid for En-Nesyri is not something they will pull the trigger on for now.
West Ham are considering their options and are looking at other potential striker targets in the market.
David Moyes wants to bring in a striker and the Hammers are intent on bringing in one in the final two weeks of the window.
It remains to be seen whether they make another move for the Sevilla hitman later in the window if they fail to secure another target.