If elected, Giuliani would reportedly use that as an intermediate step toward another White House run in 2012.
"Rudy has a history of making up his own mind and has no problem speaking it," a spokeswoman for Giuliani told the Daily News. "When Mayor Giuliani makes a decision about serving in public office, he will inform New Yorkers on his own."
Gillibrand, since taking the position in the Senate earlier this year, has been working to drum up support to overturn the military's ban on openly gay service members. Last month Gillibrand proposed an 18-month moratorium on enforcement of the ban but had to withdraw it from a defense spending bill when it became clear it would be blocked by a Republican filibuster.