According to Australian news outlet The World Game, the midfielder has attracted the attention of the two clubs after an impressive World Cup campaign with the Australia national team. While the Socceroos were eliminated in the group stages, the 27-year-old put in three promising displays and could soon be on the move.
However, Mooy still has two-and-a-half years left on his Huddersfield contract so would not be available for anything less than £20m - which is double the amount the Yorkshire Terriers paid Manchester City for the midfielder's services.
Newcastle boss Rafa Benitez has been an admirer of Mooy for the past two years, when the Magpies were battling with Huddersfield in England's second tier. In fact, the Australian scored on two separate occasions against the north east side in 2017.
However, the World Game state that Huddersfield's high asking price, along with Newcastle owner Mike Ashley's financial limits on the club, could make it difficult for Benitez to make a significant offer.
Meanwhile, West Ham have been very busy during this transfer market, spending around £90m on five players this summer. The Hammers have already bolstered their midfield with the signing of Jack Wilshere, but with Mark Noble aged 31 and Pedro Obiang seemingly set to leave the club, there could be room for one more midfield acquisition.
Mooy joined Huddersfield on an initial loan move from Manchester City in 2016, and made a £10m permanent switch to the John Smiths' Stadium after helping the club gain promotion to the Premier League.
The Australian is very highly-regarded in Yorkshire, and the club have been trying to tie the midfielder down to a new deal since the end of last season.