Bournemouth have signed Artur Boruc on a permanent deal following his release by Southampton.
Morgan Schneiderlin will only leave Southampton this summer for Champions League football.
Hammers boss Sam Allardyce has been looking to bring in reinforcements during the January transfer window to aid his side's fight against relegation from the Barclays Premier League.
However, an offer for McCormack has been rebuffed, Leeds announced on Friday night.
A statement on www.leedsunited.com 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."
Scotland international McCormack is the Championship's leading scorer this season with 17 goals, one more than Jordan Rhodes of Blackburn. The 27-year-old was also made Leeds captain just last week.
Leeds 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."
Managing director David Haigh, who in August gave McCormack a new deal amid interest from Middlesbrough, added: "As a club we showed our intentions as far as Ross is concerned during the summer."
Haigh is currently attempting a takeover at Leeds with his own consortium, having been part of the GFH Capital group which bought Leeds from Ken Bates in December 2012.
West Ham are third from bottom in the Premier League with 18 points, the same amount as the two teams below them Sunderland and Cardiff, and one behind Fulham and safety.