Mooy became Huddersfield’s record signing when he joined the Yorkshire club following his £10 million move from Manchester City last summer.
He signed a three year contract when he joined and is likely to be offered an extended deal to stay.
The 27-year-old is Huddersfield’s best-paid player on £32,000 a week, and West Ham can not only match the figure, but can also double those wages.
He has impressed during his first season in the Premier League, and as a result is attracting plenty of interest.