The Hammers have made a free-scoring start to the new Premier League season, netting a joint league-high 10 goals from their opening three games and amassing seven points in the process.
However, manager David Moyes is still keen to bolster his forward options and Sky Sports News reports that they are now closing in on Vlasic.
The 23-year-old already has some Premier League experience having joined Everton in 2017, although he lasted only one season with the Toffees and made just 19 appearances across all competitions before being shipped out on loan.
Vlasic has since rebuilt his career at CSKA Moscow, and was part of the Croatia squad at this summer’s European Championship.
West Ham are keen to wrap up the deal in the coming days, with this summer’s transfer window closing at 11pm on Tuesday night.
The Hammers are also understood to still be interested in a late £15m deal for Jesse Lingard, who scored nine goals in 16 appearances while on loan at the club last season.