SunSport understands the French side have rejected the offer as they want £11.5m and the Hammers are now considering a renewed bid.
Gameiro, 23, is one of the hottest strikers of Le Championnat.
A regular for France’s youth teams and the Under-21 side, he is now expected to get his first senior call-up next month from France boss Laurent Blanc.
He bagged 17 league goals last season and caught the eye of several major European clubs.
Under-fire Hammers boss Avram Grant is desperate to strengthen his squad after back-to-back losses in their first two games this campaign.
Gameiro has two years left on his contract and Lorient are ready to let him go but are driving a hard bargain.
Grant has at least been boosted with the news defender Matthew Upson will be fit for Saturday’s visit to Manchester United.
He was forced off against Bolton on Saturday after being kicked in the face by Kevin Davies.