The People says the Morocco international's agents held talks with Upton Park officials in London on Friday. And Chamakh has been won over by the offer of a contract until 2013 - plus a wage of £2.6million a year after tax.
Bordeaux have accepted West Ham's £7m bid for the 25-year-old, who would be a free agent next year.
"I have crossed the Arsenal option off my list," he said.
Hammers boss Zola is desperate to land Chamakh despite bringing in frontman Alessandro Diamanti.
Zola said: "Chamakh is a player we're interested in. We're trying everything we can."