The 27-year-old defender was subject to a transfer proposal from Newcastle that was rejected by Wolves. According to The Telegraph, The Magpies offered midfielder Elliot Anderson plus a cash sum for Kilman.
Anderson ultimately left to join Nottingham Forest for £35million instead as West Ham United swooped in to agree a deal with Kilman.
According to transfer expert Fabrizio Romano, West Ham’s new £40million bid for the defender is expected to be accepted with Kilman already agreeing personal terms.
Romano tweeted: “West Ham are closing in deal to sign Max Kilman from Wolves! New bid worth £40m expected to be accepted soon, agreement almost done. “Kilman already agreed on personal terms as Julen Lopetegui wants him at all costs, as revealed weeks ago. Here we go, soon.”