Sky Sports understands the bid was in the region of £3 million plus add-ons. West Ham are expected to come back with a new offer over the weekend.
Sky Sports revealed earlier on Friday that the Hammers had made a bid for the Scotland international striker, who is the top scorer in the Championship with 18 goals to his name already.
McCormack signed a new long-term deal last summer, when Leeds fended off multiple bids from rivals Middlesbrough for the the 27-year-old.
And on Friday night a statement on Leeds' official website read: "Leeds United have rejected an offer from West Ham United for striker Ross McCormack.
"The London club made an offer for the player on Friday afternoon which was rejected by the club's board."
Separately, Leeds' Managing Director David Haigh tweeted: "As a club we showed our intentions as far as Ross is concerned during the summer."
And chairman Salah Nouruddin said on Twitter: "I'd like to reassure all #lufc fans that we're working hard for the club and can confirm we've rejected an offer from West Ham for Ross."
Sam Allardyce's Hammers, who are desperate to bolster their squad as they battle to avoid relegation, saw McCormack as a potential solution to their goalscoring problems.
McCormack has just been made captain at Elland Road by manager Brian McDermott.