The Hammers are yet to make their first move in the transfer market in spite of having pocketed £105m through the sale of Declan Rice to Arsenal.
Veteran manager David Moyes wants as many as two midfield signings, one of whom is Ward-Prowse., who turns 29 in November.
The Southampton skipper, who has remained at St Mary’s Stadium since the very first day of his career as a senior player, has been linked with a move away following Southampton’s relegation.
However, Saints are holding on to their £40m valuation, something that the Hammers are unwilling to pay.
They believe that Ward-Prowse should warrant a fee of around £25m and are unwilling to overpay.
West Ham believe that given Ward-Prowse’s age, he will not have significant resale value and that is shaping their view.
As a result, West Ham are prepared to end their efforts to sign Ward-Prowse; the Premier League outfit have not made a single signing yet this summer.