The Hammers are eager to back new manager Julen Lopetegui in the transfer market.
Kilman, who is a long-term target for the London club, has worked with Lopetegui at Wolves.
Advertisement
Advertisement
Having played 24 times for the Spaniard, The Sun states that a bid will go in for him this summer.
However, Wolves will play hard ball and are set to demand at least 45 million, says The Sun.
One of their key issues this season was a lack of defensive stability due to injuries and other issues.