"That's not going to happen," Rubio said on CNN's "State of the Union." "I don't believe it's going to happen."
Despite Trump's tweets to the contrary, the Florida Republican said that Mueller's investigation into alleged Russian interference in the 2016 election and potential collusion with members of Trump's orbit is fair. Rubio added he has "no reason" to have questions about the fairness of Mueller's investigation, and does not plan to change his mind on that unless presented with evidence.
"His reputation is stellar," Rubio said.
Rubio called on Trump and the administration to let the investigation go forward and not cast aspersions.
"The best thing that could happen for the President and the country is a full and credible investigation," Rubio said. "If we want to put all of this behind us, let's find out what happened, let's put it out there and let's not undermine the credibility of this investigation."
Rubio serves on the Senate intelligence committee, which is also investigating Russia's role in the election.
"These investigations continue to move forward," Rubio said. "At its core, the Senate's work is about Russian interference and how they did it. And if it involved working with Americans whether wittingly or unwittingly that needs to be a part of it."
Rubio also defended his Republican colleagues in the Senate, who are drafting a health care bill behind closed doors. He said the closed off process was not particularly out of the ordinary and that any bill should be eventually subject to open debate and change.
"That bill is not going to go from that group to the President's desk," Rubio said. "That bill has to at least have a vote in the Senate, and I hope it's a vote that allows plenty of time for debate, analysis and changes -- and input. And if that's the process we follow, it'll be fine."
Alternatively, Rubio said the bill should not go to a vote without the opportunity for debate and input.
"If it's an effort to rush it from a small group of people straight to the floor on an up or down vote, it'll be a problem," Rubio said.
He again stressed that whatever the Republican group produced would "only be a starting position."