President Reagan, who has been pressured to name a homosexual to his new national commission on AIDS, is expected to appoint to the panel Dr. Frank Lilly, a gay genetics professor, according to White House sources.

Lilly, who chairs the genetics department at the Albert Einstein College of Medicine in New York, said yesterday he had been interviewed by the White House for membership on the panel but had not been informed whether he had been appointed. The full panel -- expanded from 11 to 13 members last week -- is expected to be named Thursday.

Lilly's appointment would follow a bitter disagreement over the makeup of the commission, which will advise the White House on the public health dangers and the impact of acquired immune deficiency syndrome on society. While gay activists and several leading AIDS researchers have argued that the panel should include a homosexual, the administration has indicated it would not make an appointment based only on a person's sexual preference.

Gary L. Bauer, a domestic policy adviser to the president, in May said, "This administration has opposed in the past appointing people to jobs or giving them assignments solely because of race or sex. I just don't know how one can philosophically believe that and then turn around and appoint somebody based on sexual preference."

Bauer would not comment yesterday.

Several AIDS researchers and public health experts wrote President Reagan this spring to protest the administration's stance, arguing that the population most affected by the disease should be represented. Nearly 75 percent of the more than 37,000 Americans diagnosed with AIDS are homosexual men, according to public health statistics.

Lilly, reached last night at his home in New York, said he had answered "a few questions" in a telephone interview with the White House. "I know that I'm under consideration but I haven't been told definitely," he said.

Lilly, who served on a National Academy of Sciences panel on AIDS, identified himself as gay but said, "I have never considered myself to be a gay activist."

Urvashi Vaid, a spokesman for the National Gay and Lesbian Task Force, said of the expected appointment: "Obviously, we're very pleased it's a gay person and someone with some expertise on the disease."

Late last month, President Reagan appointed Dr. William Eugene Mayberry, chairman of the board of the Mayo Clinic, to head the commission, which was established by executive order. The panel is mandated to issue a preliminary report within 90 days of its full appointment and release a final report next June.

The panel is ordered to recommend measures that federal, state and local officials can take to protect the public from the AIDS virus, work towards finding a cure, and improve care for AIDS victims.