HOWARD Koeppel, the gay car dealer who was Rudy Giuliani‘s roommate in 2001, predicts the former mayor will not run for governor next year. At the recent book party for “Betrayal: The Life and Lies of Bernie Madoff” by Andrew Kirtzman, Koeppel was overheard telling Ch. 4’s Melissa Russo, “Rudy is not run ning.” Koeppel told us yesterday, “He [Giuliani] told me he would never want to be governor. The state is unmanageable, and having to deal with the likes of Shelly Silver . . . That’s what he told me when he was living with me.” Giuliani and Koeppel also shared their apart ment with pianist Mark Hsiao, who mar ried Koeppel last May at a ceremony Giuli ani failed to attend. “There’s a lot of issues to keep Rudy from running,” Koeppel said. For one thing, his former Police Commis sioner Bernard Kerik is facing trial on cor ruption charges. A source close to Giuli ani said, “He is going to make a decision some time after this year’s election. Clearly, a lot can change in eight years.”