He told BBC Sport: "I have talked with Omega [about China] for over a year and will continue to talk to Omega. I have and will go to the places I and China do business and ask for help."
Omega is one of 12 brands that are "worldwide Olympic partners" for the Beijing games and it has been the official timekeeper for every Olympics since 1932.
Nick Hayek, the chief executive of the Swatch Group, which is owned by Omega, told the BBC that the company had discussed the issue with Clooney, adding that it had full respect for his "strong engagement in the fight for the good cause" and shared his opinion, "especially concerning Darfur".
However, he said company policy was not to get involved in politics: "We are partners of the athletes and the [International Olympic Committee], not of governments, which is why we were present during the boycotted games of 1980 and 1984."
In Darfur, pro-government Arab militias have been accused of carrying out a campaign of ethnic cleansing against non-Arab people. During the last five years of conflict, more than 200,000 people have been killed and over 2m forced from their homes.
China, which is a major trading partner of Sudan, has vetoed the United Nations' attempts to force the country to allow peacekeepers into the region.
When asked whether Omega would speak out on China's association with the Sudanese government, Hayek told the BBC: "Of course, it is a continuous process but we do it the Swiss way of 'little strokes fell great oaks'. We make our point directly to our high-level contacts and not by jumping in at every headline."
Hayek also said Omega will continue to monitor the situation in Darfur and China's involvement.
Omega said that there is no indication that its relationship with Clooney will come to an end.
China's record on Sudan has already come under pressure from Steven Spielberg's resignation as artistic director of the Games in February while all Olympic sponsors were criticised for their refusal to press the host nation by US campaign group Dream for Darfur last November.