Giuliani prefers Sen. Rubio for vice president

"I like them all ... [Wisconsin Rep.] Paul [Ryan] would be a terrific candidate. I kind of prefer Marco Rubio," he said Giuliani on CBS's "This Morning."

Giuliani, who ran against Romney during the 2008 Republican primary, said he was in favor of Rubio because the Florida senator could bring support from the Hispanic community and young voters to GOP the ticket.

When asked what the presumptive Republican nominee thinks about Rubio, Giuliani said, "I don't know. I think he respects them all. I think he respects [former] Gov. [Tim] Pawlenty and Sen. [Rob] Portman [(Ohio)]. I think they'd be excellent choices."

"The reason I sort of lean towards Marco is I like the idea that he's very smart. I like the idea that he's a terrific debater and speaker. They're all of that, but he adds the element of outreach to the Hispanic vote and outreach to young people and we need help. Frankly, the Republican Party needs help in both those areas," he said.

The former mayor told CBS that in terms of women candidates, former Secretary of State Condoleezza Rice would be a "very exciting choice."

Rice has been mentioned as a possible vice presidential contender, but she has repeatedly denied interest in political office. Some conservatives have raised concerns about her stance on abortion, but many Republicans have praised her service and qualifications.

Giuliani said the "most important" quality for a vice president is that he or she be prepared to step into the president's role if necessary," saying that Rubio is "absolutely" qualified.

"[V]ice president's don't win for the president, they lose for the president," he said.