West Ham have had a £31m bid for Lyon striker Alexandre Lacazette rejected by the Ligue 1 side, Sky sources understand.
The Hammers are keen to add to their attacking options and it is understood they were rebuffed by Bournemouth on Monday when they made an offer for striker Callum Wilson and winger Matt Ritchie.
Sky sources understand that Slaven Bilic is also interested in Liverpool forward Christian Benteke and Marseille's Michy Batshuayi, as well as Lacazette.
The 24-year-old was a target for Newcastle last season, both in the summer and January, and he has been a prolific goalscorer for his club over the last three seasons.
He scored 27 times in 33 league appearances in 2014-15 and added a further 21 league goals this season and only signed a new four-year contract at Lyon in August.
West Ham's co-owner David Sullivan said last week, as the club was preparing to say farewell to the Boleyn Ground, that a number of bids for strikers had been made or were being plotted.
They have already agreed a deal to bring Norway midfielder Havard Nordtveit to the club when the transfer window opens.