The centre-back signed for the Hammers in 2022 from Paris Saint-Germain and won the Europa Conference League in his debut season.
Kehrer played in both the semi-finals and final for West Ham en route to European glory, their first major trophy since 1980.
However, the German has struggled for game time in the current campaign and looks set to on his way out of east London.
Kehrer has told the Hammers he wants to leave after playing just 19 Premier League minutes this season.
The 27-year-old has not made a single league start and was an unused substitute for 11 consecutive matches.
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Kehrer has played in the Europa League and Carabao Cup for West Ham but it's clear he's not a first-choice option under David Moyes.
Kurt Zouma, Konstantinos Mavropanos and Nayef Aguerd are all preferred options at the heart of the defence.
Should he sign for Monaco, Kehrer would join a side who currently sit third in Ligue 1 at the halfway point of the season.
West Ham are enjoying a strong season of their own, with the Hammers securing two huge wins towards the end of 2023.
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Moyes' side beat Manchester United 2-0 before repeating the same score line away at Arsenal to take them to sixth in the table.
Although they may be seven points outside of the top four, West Ham are still firm contenders to seal a top seven finish.
The Europa League last 16 awaits them in the coming weeks as they eye back-to-back triumphs in Europe.
Kehrer looks set to leave West Ham in January though, just a year-and-a-half after he first joined.