Such a private sit-down with a Cabinet member is rare, but "we're very persistent," Brewer spokesman Matthew Benson told The Arizona Republic.
Brewer, who is in Washington for the National Governors Association meeting, is scheduled to meet Sebelius Monday.
She wants to drop 280,000 people from the Arizona Health Care Cost Containment System and is seeking further "common-sense" changes, Benson said, such as ending coverage for taxi rides to doctors and charging patients who miss appointments.
"These are reforms that have long been part of the private healthcare system," he said. "But a good number of these would require federal approval."
Arizona's Medicaid program covers 1.3 million people and costs the state about $2.5 billion annually.