The Hammers are in the market for further additions to David Moyes’ squad before the transfer window slams shut.
A potential swoop for Lingard, who spent last term on loan at the club, has been floated, but West Ham are pressing ahead with a move for Vlasic.
It is claimed that they see Vlasic as a better option than Lingard, with Manchester United looking for £25m for a player into the final year of his deal.
Vlasic, five years younger than Lingard, is viewed by West Ham as a better bet and they are close to signing him for a fee of £25.7m.
West Ham are moving towards finalising the capture of the 23-year-old and the agreement will also contain a number of add-ons.
The Hammers will hope that Vlasic can hit the ground running at the London Stadium, while he will also offer boss Moyes a fresh option in the Europa League.
Vlasic has had a prior spell in English football, spending two years at Everton but failing to make an impact.