The Hammers had a £22.5 million bid plus £4.5m add-ons for the forward rejected last week, with Sevilla upping their demands to £35m.
But David Moyes want to avoid making the same mistake they made with Sebastien Haller and will not pay over the odds for their next frontman.
He is also mindful not to repeat his choice of Jordon Hugill who is struggling at Championship club Norwich after a £3m move.