Sen. Rand Paul Randal (Rand) Howard PaulSecond GOP senator to quarantine after exposure to coronavirus GOP senator to quarantine after coronavirus exposure The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill MORE (R-Ky.) late Tuesday said he probably won’t make a decision about whether to run for president in 2016 until early next year.

“I haven't decided yet but I'm thinking about it and discussing it with family. We won't make a decision probably until early next year,” Paul said on Fox News’s “On the Record.”

He has previously said he would decide after the 2014 midterm elections.

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Paul also rejected claims that Sen. Marco Rubio Marco Antonio RubioSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Florida senators pushing to keep Daylight Savings Time during pandemic Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll MORE (R-Fla.), another potential 2016 contender, took a shot at him on Tuesday during a speech at the National Press Club.

“Marco and I are good friends,” Paul said. “So, I think I would be the first to know if he were taking a shot at me … I think, no matter who runs, I'm sort of a Republican who believes in peace in commerce with all Republicans and I'm going to try to keep it on a high plane.”

Without mentioning Paul by name, Rubio said he doesn’t think it’s effective to run for president and another office simultaneously.

"If someone decides to run for president of the United States, you run for president of the United States," Rubio said. "I don't believe you can run effectively for an office of that magnitude while having some exit strategy in mind."

Paul is up for reelection in 2016, and has said he would want the opportunity to run for both the Senate and the White House at the same time.

Kentucky law currently prevents candidates from running for two offices, but Paul hopes he can change the law in time.