McCormack, 27, who was recently named captain of the Yorkshire club is believed to be a key target for Hammers boss Sam Allardyce ahead of next week's transfer deadline.
So far this season, the Scotsman has scored seventeen goals in twenty-one league appearances.
The bid is believed to be in the region of £3m.
McCormack joined Leeds United from Cardiff City in 2010, having scored thirty goals in eighty-nine appearances for the Bluebirds.
Brian McDermott named Ross McCormack as captain last week, having decided to take the captaincy away from midfield Rodolph Austin.
It appears unlikely that Brian McDermott or chairman Salah Nooruddin will accept this initial bid from West Ham.
West Ham co-owner David Sullivan confirmed in December that the club would be adding at least one more striker to their books, as evidenced by attempts for loan deals to bring Ishak Belfodil of Inter Milan and Marco Borriello of Roma to Upton Park.
Their latest target is the current Championship top scorer, but Leeds United are reluctant to sell, as Cagliari president Massimo Cellino continues to lead attempts to complete a takeover of the Whites.
McCormack signed a new four-year deal with the Elland Road outfit last summer, so it is thought that an offer of £3m would be deemed unsatisfactory.
However, it is expected that the East London club will return with further bids, should this attempt be unsuccessful.
image: © Jon Candy