Affirmation, with more than 2,000 gay, lesbian and transgender members, is not recognized by the church, which at one time labeled homosexuality as a problem that required help.
"Although there are many areas of hurt and disagreement that have separated us, there are many more areas on which we can find agreement, and in doing so, become a blessing in the lives of many of the Saints, both straight and gay," the group wrote in its invitation to Thomas S. Monson last week.
Monson assumed leadership of The Church of Jesus Christ of Latter-day Saints last Sunday following the death of its previous president, Gordon B. Hinckley.
Such a meeting with Monson and his counselors -- a triumvirate known as the First Presidency -- would be unprecedented, said David W. Melson, the group's assistant executive director.
"This was something we've talked about for a while," Melson said. "With the death of President Hinckley and the installation of new church leadership, it seemed like the appropriate time."