Kilman has been Julen Lopetegui’s top centre-back target this summer as the West Ham boss pushed to sign him ahead of the new season
Wolves rejected an initial offer from the Hammers but finally accepted a bid of £40m from the east London club on Thursday.
A general agreement is in place between the two clubs and Kilman has been undergoing a medical.
The Wolves captain is expected to complete the medical checks the end of the day to get closer to completing a deal.
West Ham are also expecting the centre-back and his representatives to sign off on the personal terms of a contract.
The two clubs will hope to finalise the paperwork of the agreement in the next 24 to 48 hours.
The Hammers have optimism that Kilman’s arrival can be finalised over the course of the weekend.
