It has been reported by the French publication that the Hammers made an offer of €20 million (£14.2m) for the Tunisia international defender.
However, that bid has been rejected by Monaco, according to the report, as the French club want more money to part company with the centre-back.
West Ham face competition from a number of clubs to secure the signature of Abdennour, according to various reports.
Tottenham Hotspur and Liverpool both are monitoring Abdennour, according to Foot Mercato.
Abdennour was one of the best players in the 2014-15 Ligue 1 campaign, helping Monaco finish second.
The 25-year-old Tunisia international created three chances in 18 league appearances, while having a pass accuracy of 84% and shot accuracy of 100%.
The centre-back won 40 headers, three dribbles and 20 tackles in those 18 Ligue 1 matches.