The English Premier League outfit have invited Duke to train at Upton Park with Sam Allardyce's squad and the Mariners have revealed the 22-year-old striker will leave Australia on Saturday for a week with the London-based club.
The interest from West Ham comes after Duke made his Socceroos debut at the East Asian Cup last month.
Duke scored two goals and was one of only four players to start all three of Australia's matches in the tournament in South Korea.
The powerfully built forward had a breakout season for the Mariners during their 2012/13 A-League championship-winning campaign, scoring eight goals in 28 appearances in all competitions.
Central Coast expect Duke to return to Australia on August 17 but said in a statement they would 'update fans and media with any further developments... should they occur'.
West Ham finished 10th in the 2012/13 Premier League season and will kick-off their new campaign at home against Cardiff next week.
The London club has had a strong connection with Australia in the past with Richard Garcia, Hayden Foxe and Michael Ferrante all having spent time at Upton Park, while 19-year-old Australian forward Dylan Tombides is currently part of West Ham's youth set-up.