The Hammers are said to have made an offer of £2 million for the 20-year-old only to see Hamilton knock back their advances.
The Scottish Premier League side are desperate to keep hold of Hendrie, who is regarded as one of the division's finest talents, but doing so is becoming increasingly difficult.
Celtic are also said to be interested in signing him by the Daily Mail, while Swansea City and Crystal Palace have also watched the left-back in recent weeks.
If Hendrie were to arrive at the Boleyn Ground this month he would probably be considered back-up in his initial campaign at the club.
Aaron Cresswell has established himself as the Hammers' first-choice in that position, but Sam Allardyce seemingly believes that Hendrie has the ability to provide him with serious competition in the future.