The 27-year-old, who has been capped on 16 occasions by the United States, has been with the Red Bulls since 2016, first representing their second team before becoming a key player for Chris Armas's side.
According to Sky Sports News, the Hammers offered £382,000 in order to loan the centre-back for the remainder of the season with a £3.4m purchase option this summer.
However, the report claims that the MLS outfit have rejected the English club's opening bid.
Long was also linked with a possible switch to the London Stadium in last summer's transfer window but issues over a work permit are believed to have scuppered his hopes of moving to the Premier League.
West Ham will be looking to win in the Premier League for the first time since New Year's Day when they welcome runaway leaders Liverpool on Wednesday night. body check tags ::