Since former Wolves boss Julen Lopetegui was appointed as the successor to David Moyes, it has been widely claimed that the Spaniard is keen on a reunion with one of his former players.
The 27-year-old has established himself as one of Wolves' key men, missing just one Premier League fixture in two seasons and being named as captain.
According to Sky Sports News, the Hammers have proposed a deal worth £25m for the centre-back.
However, that offer will almost certainly be rejected with Wolves known to be looking for at least £40m for a player who still has four years left on his contract.
Former club Maidenhead United are due a sizeable percentage of any deal fir Kilman, who has also been linked with Manchester United and Tottenham Hotspur.
Southampton chasing departing Fulham attacker
Meanwhile, Southampton are allegedly looking to strengthen their first-team ranks with the addition of Bobby Decordova-Reid.
The Saints have just secured a return to the Premier League at the first opportunity through defeating Leeds United in the Championship playoff final.
Russell Martin has already acted to add veteran playmaker Adam Lallana to his squad, and it appears that another experienced head may make the move to St Mary's.
According to The Sun, the South-coast outfit are interested in exploring a deal for Decordova-Reid, who is available on a free transfer.
His five-year stint with Fulham has just to an end, the 31-year-old contributing 32 goals and 18 assists from his 209 appearances in all competitions.
Eight of those contributions came in the Premier League during 2023-24, seemingly convincing Southampton that the versatile attacker could be a useful signing.
Arsenal to lose youngster on free transfer
Arsenal have reportedly been unable to convince Amario Cozier-Duberry to commit his future to the club.
The 19-year-old has been highly rated at the Emirates Stadium for some time, yet Mikel Arteta failed to hand him any senior minutes last season.
With his contract expiring at the end of June, it left the England Under-19 international with a decision to make over the next phase of his career.
According to transfer expert Fabrizio Romano, the prospect has opted to seek pastures new in search of regular action.
Clubs around Europe are said to be looking to hold discussions with the winger, who is likely to attract interest from some high-profile clubs.