The Hammers are working without Nayef Aguerd for the next few weeks while he represents Morocco at the African Cup of Nations, and the ex-Rennes man is also being linked with a move to Saudi Arabia.
West Ham reinforced their backline in the summer with the capture of Dinos Mavropanos from Stuttgart, but another centre-half is expected to arrive if Aguerd does end his stint at the London Stadium.
According to The Guardian, West Ham boss David Moyes has been keeping an eye on Kilman for some time, although the Europa Conference League champions will not capture the 26-year-old on the cheap.
Kilman's contract at Molineux runs until the summer of 2028, and Wolves are supposedly ready to demand as much as £40m to let their 6ft 4in captain leave before the end of the winter window.
Kilman has two goals and two assists under his belt from 129 matches for Wolves in all competitions, scoring once in 20 Premier League starts for Gary O'Neil's side this term, and he has not missed a single minute of top-flight action in 2023-24 so far.
From potential outgoings to possible incomings at Molineux, Wolves are believed to be one of a number of clubs plotting a loan move for Liverpool attacker Fabio Carvalho.
The Portuguese youngster is back at Anfield following an unsuccessful loan spell with RB Leipzig in the first half of the season, where he totalled just 360 minutes across 15 appearances and failed to bank a single goal or assist.
Carvalho is expected to be sent back out on loan for the second half of the campaign and has been linked with a move back to the Championship, with Leeds United, Hull City, Leicester City and Southampton all named as possible suitors.
However, the Daily Mail reports that Carvalho could be offered the chance to stay in the Premier League, as Wolves and former club Fulham are both interested in taking him on a temporary deal.
Liverpool will want to ensure that the 21-year-old receives ample game time in the wake of his disappointing Leipzig spell, though, which could see the Reds favour doing business with a Championship club.
Carvalho shone for Fulham during their promotion-winning 2021-22 campaign and has since scored three goals in 21 games for Liverpool, who have him under contract until 2027.
Over at the Allianz Arena, Bayern Munich have apparently opened discussions to sign out-of-favour Paris Saint-Germain defender Nordi Mukiele.
The 26-year-old has only enjoyed limited appearances under Luis Enrique this term, having fallen further down the rearguard pecking order since the summer signings of Milan Skriniar and Lucas Hernandez.
Mukiele is now facing added competition from January signing Lucas Beraldo, and he has made just four Ligue 1 starts in the 2023-24 campaign, being an unused substitute in each of their last three top-flight games.
According to the Daily Mail, Bayern are now in talks over a deal for Mukiele, who is one of three defensive targets for the German champions alongside Tottenham Hotspur's Eric Dier and Chelsea's Trevoh Chalobah.
Dier is still believed to be Bayern's priority, but Thomas Tuchel's side are yet to agree a fee with Tottenham and could ramp up their efforts to sign Mukiele if a move for the Englishman falls through.
Mukiele made 100 Bundesliga appearances during his successful spell with RB Leipzig and boasts four assists in 35 matches for PSG, where his contract runs for another three-and-a-half years.
Speaking of backline rejigs, Premier League basement battlers Sheffield United have supposedly earmarked Leicester City goalkeeper Danny Ward as an ideal addition to their squad in January.
With Wes Foderingham in between the sticks, Sheffield United have shipped a Premier League-high 49 goals in the 2023-24 campaign, and their defensive woes have contributed significantly to their meagre nine-point haul this season.
Chris Wilder's men have already strengthened their offensive ranks with the signing of Ben Brereton Diaz on loan from Villarreal, but attention is now turning to defensive acquisitions for the 20th-placed Blades.
Another report from the Daily Mail claims that Sheffield United have now made enquiries over a deal for Ward, who is yet to make a single appearance for Leicester City in the 2023-24 season.
Ward kept six clean sheets in 26 Premier League games for Leicester during the 2022-23 Premier League campaign, but new Foxes head coach Enzo Maresca has preferred Mads Hermansen in between the sticks so far.
The Wales international only has 18 months left to run on his Leicester deal, but should Sheffield United fail in their efforts to prise him away from the King Power Stadium, Anderlecht and Denmark veteran Kasper Schmeichel could be targeted instead.