The 30-year-old has made nine Premier League appearances so far this season, but he has started only one of their last eight top-flight games since the beginning of October.
Coufal has, however, featured more regularly in the Europa Conference League, starting all six group-stage matches, while he also began the EFL Cup third-round clash against Blackburn Rovers which ended in defeat on penalties.
The Czech Republic international seems to have fallen behind highly-rated academy graduate Ben Johnson and summer signing Thilo Kehrer under David Moyes, and his long-term future at the London Stadium is believed to be uncertain.
Coufal is under contract in East London until the summer of 2024 and the Hammers have the option to extend his deal by a further year.
According to Sky Sports News, Coufal has attracted interest from Bundesliga club Bayer Leverkusen, while two unnamed Premier League teams are also in the race for his signature.
The report adds that West Ham are prepared to entertain 'concrete offers' for Coufal, but they are reluctant to sell any defenders in January due the injuries they have in this department.
Coufal joined West Ham in the summer of 2020 from Slavia Prague for around £5m and he has since made 87 appearances across all competitions, providing 12 assists.
Leverkusen's first-choice right-back over the last two years has been Jeremie Frimpong, who has established himself as a key player at the BayArena since joining the club from Celtic in January 2021.
However, the 22-year-old has attracted interest from the likes of Manchester United and Chelsea and one report claims that he is open to linking up with fellow Dutchman Erik ten Hag at Old Trafford.
A potential departure for Frimpong may see Leverkusen step up their interest in Coufal, who could join up with compatriot Patrik Schick should a switch to the BayArena come to fruition.
Elsewhere at West Ham, Moyes is closing in on his first signing of the New Year as Sao Paulo defender Luizao has allegedly completed a medical in London ahead of joining the club on a free transfer.
The 20-year-old is said to have agreed to sign a three-and-a-half-year contract until the summer of 2026 and he is set to link up with the club's development squad.