Some 240 adults will be injected with the vaccine in trials which began today.
Andrew Cuthbertson, CSL's research and development director, said the vaccine should be proven by late September, reports News.com.au.
"As soon as I have confirmation that the vaccine is safe and effective, I will ensure it can be rolled out to the community," federal Health Minister Nicola Roxon said.
The adult trials are testing the appropriate dose of the vaccine.
"It will be available when the government decides how to roll it out," Cuthbertson said.
"There is a clear distinction between CSL's role, which is to do the research, develop the vaccine and make it in large amounts and make it available to government - and government will then decide what the roll out will be.
"There may be a point where our government feels the threat justifies moving forward in deploying the vaccine," he added.
CSL spokeswoman Rachel David said there was "no additional safety risk in rolling out the vaccine" in September or October.
Cuthbertson said CSL was "confident that the safety profile of this vaccine will be very similar to our normal seasonal vaccines".
"We will be supplying other countries but we would supply Australia with the vaccine, and then the rest of the world," he said.
Meanwhile, H1N1 swine flu has claimed lives of more than 700 people across the globe since it broke out four months ago, the World Health Organization (WHO) has said.