Hammers boss David Moyes wants to bring McTominay to the London Stadium and his side have lodged a bid.
The offer came in at £30m and was quickly turned down by Manchester United, who feel that it undervalues McTominay.
And it is claimed that there is a feeling West Ham will need to go up to £45m if they are to get the job done with a McTominay bid.
Whether the Hammers are prepared to go that high is unclear.
However, West Ham are flush with cash after selling Declan Rice and Gianluca Scamacca, while Nikola Vlasic is also set to depart.
McTominay’s Manchester United team-mate Harry Maguire is also wanted by West Ham.
The Hammers have had a chaotic transfer window in terms of their strategy this summer, with disagreements behind the scenes over which targets to chase.