The five-year contract would come with restrictions, however, including a spell in rehab and monitoring by the company's headquarters in Costa Rica for two months to prove the star is not taking drugs, as recent tabloid pictures have indicated.
The poker site has also asked Moss to participate in a nine.com-sponsored anti-drugs campaign aimed at students.
The offer was faxed to Moss' agents last week and representatives of the star have yet to comment on the deal.
Nine.com conducted a focus group, which found that customers were not phased by the allegations that the 31-year-old star took cocaine.
Jack Abrams, a nine.com spokesman, said: "We did a quick focus group with some customers to see if they would be offended in any way and the response was an overwhelming, 'No -- please get Kate Moss as your spokesperson'."
So far, the Croydon-born supermodel has lost lucrative contracts from H&M, Burberry and Chanel due to the tabloid revelations. Other brands including Christian Dior are said to be considering their future use of the model.
The only brand to publicly stand by Moss is cosmetics giant Rimmel, which praised the star last week for issuing an apology over the allegations.
If you have an opinion on this or any other issue raised on Brand Republic, join the debate in the Forum.
This article was first published on brandrepublic.com