Paul told reporters, however, that "it will probably be two years before we have a serious discussion" about a presidential run.

He also said that he hasn't yet pursued a law change in the state, to allow him to run for two offices at the same time.

"We have not looked at that or discussed that with anybody," he said. "The only thing that we have made absolute plans is that I have formed a reelection committee and I will run for the U.S. Senate."