"I think we have a lot of Republican governors. I like Chris Christie, I like Bobby Jindal," John McCain said. "I like a number of those people who have succeeded in states with Republicans and Democrats."
Leno then asked Meghan McCain, who said, she's still deciding.
"I like Chris Christie but we got into a fight and now I don't like him anymore," Meghan said.
"What did he hit on you?" Leno asked.
"I just said he may not be my top contender for 2016 because I'd like to see the field," Meghan said. "I still like Marco Rubio and he did not like that answer. I think he hates me."
Louis CK, who was also on the program, chimed in, "I think he (McCain) should run. I think he should just say forget the Democrats and the Republicans, and just run as John McCain."
Leno also asked if Sen. McCain would run for reelection in the Senate.
"I am looking at it very seriously, very seriously," John McCain said. "I think a lot is going on and I'm at the top of my game."
Leno and McCain then discussed the Senate. "You've been in the Senate now for almost 87 years," Leno joked. What's the biggest change?"
"Lack of good relationships," Sen. McCain said. "Too much polarization, too much anger, it's really kind of an unfortunate thing."
Finally, Leno and McCain talked about the Winter Olympics in Sochi.
"Now you and Putin aren't great friends, right?" Leno asked.
"Well, Vlad goes around without his shirt on all the time and I can't do that anymore," McCain joked. "But the problem with Vlad is that he'd like to see the good old days of the Soviet Union it seems to me, but let's hope the Olympics go well."
Jimmy Fallon's "Tonight Show" tenure begins Monday, Feb. 17 on NBC.