Gilmore, who briefly sought the 2008 Republican nomination before dropping out, said in an interview with the newspaper that he planned to make the announcement in the first week of August.
Gilmore, 65, served one term as Virginia's governor, from 1998 to 2002, and was the chairman of the Republican National Committee in 2001.
He is also a former U.S. Army intelligence officer and later headed the Gilmore Commission, a congressional panel that advised Presidents Bill Clinton and George W. Bush on domestic capabilities for responding to terrorism involving weapons of mass destruction.
