Giuliani's pro-abortion position is a stark contrast to the rest of the Republican field, which may be split on embryonic stem cell research but pretty solidly opposes abortion.
Sarah Stoesz, President of the Planned Parenthood Action Fund, told the pro-abortion Reality Check web site that she is more concerned about promoting abortion than supporting an anomaly in a political party.
"We want to look at a candidate's broad commitment to reproductive health care," she said. "If a candidate supports abortion rights but would not fund greater to access to birth control, that would not be a candidate we would support."
That means Giuliani would need to make a strong commitment to supporting the morning after pill and pushing Planned Parenthood's goals on it.
That would include removing the age limit to purchase the Plan B drug, as teenagers cannot buy it over the counter, and forcing pharmacists nationwide to dispense it.
As a result, Planned Parenthood likely couldn't support the former mayor.
"Rudy Giuliani with respect to abortion rights has a mixed record. He was a supporter but backed away. We need someone who will stand up for reproductive health care. I don't know that we trust him on that quite yet," Stoesz said.
Instead, Planned Parenthood is more likely to back the eventually Democratic nominee as all of the party's candidates for president are uncompromisingly pro-abortion.
"We're keeping an eye on Giuliani," she said, just in case he would come around to their position more.
In the 2004 election, Planned Parenthood supported the first presidential candidate in its history when it solidly backed John Kerry. He ultimately lost to President Bush as the issue of abortion gave the president an advantage.