West Ham have submitted an improved bid for Armando Broja of £30m plus add-ons and are close to agreeing personal terms with the Chelsea striker.
Broja has told Chelsea he wants a permanent move, not another loan after spending last season at Southampton, and Everton could also bid for the 20-year-old forward.
West Ham made a £25m offer on Friday as they seek to strengthen a forward line in which the 32-year-old Michail Antonio is the only senior player.
Broja, who scored nine goals in all competitions for Southampton last season, has returned to England from Chelsea’s US tour because of an injury which is understood not to be serious.
Everton are looking for a striker after selling Richarlison to Tottenham and there has also been interest in Broja from Newcastle and Napoli.
West Ham have targets aside from Broja in attack. They submitted a €40m (£33.9m) offer for the Sassuolo striker Gianluca Scamacca last week and have held further talks with Jesse Lingard, a free agent after his departure from Manchester United.
However West Ham want Lingard to lower his wage demands, with the attacking midfielder pushing for £180,000 a week. Moyes is also trying to add more depth in midfield. West Ham are hopeful they will succeed with a €38m offer for Lille’s Amadou Onana.
Chelsea are also likely to send Tino Anjorin out on loan. Huddersfield are leading the race to sign the 20-year-old forward. Coventry, Queens Park Rangers and Norwich are also interested in Anjorin.