The groups are concerned that Bush and his super PAC, Right to Rise, "are engaged in knowing and willful violations of federal campaign finance laws." The groups are calling on Attorney General Loretta Lynch to appoint an independent special counsel to investigate potential violations.
On Sunday, Bush dismissed the allegations.
"I would never do that," he told CBS's "Face the Nation." "And I'm nearing the end of this journey of traveling and listening to people, garnering, trying to get a sense of whether my candidacy would be viable or not. We're going to completely adhere to the law, for sure. Look, politics is politics. There's always people that are going to be carping on the sidelines. And should I be a candidate, and that will be in the relatively near future where that decision will be made. There'll be no coordination at all with any super PAC."
"Face the Nation" moderator Bob Schieffer asked Bush whether he thinks the legacy of his brother, former president George W. Bush, could become a dominating subject that derails his chances.
"No, I don't," he said. "This is hard for me, to be honest with you, to — I have to do the Heisman onto my brother, that I love. You know, this is — this is not something I'm comfortable doing."
"As I tell that story, people will begin to say, 'Yeah, look, he's a Bush, that's fine. But I'm for him because he has ideas that will help me rise up,'" he added later. "And so, I don't, my brother's not going to be a problem at all. I seek out his advice. I love him dearly. I've learned from his successes."
Bush frequently uses the Heisman Trophy metaphor as a way to discuss when somebody is seeking distance from an issue. Usually he suggests that former secretary of state Hillary Rodham Clinton "can't do the Heisman" and put distance between herself and the foreign policy legacy of President Obama.
Asked what lessons he has taken from his brother's presidency, Bush cited George W. Bush's success in protecting the country but also his inability to control federal spending, partly because of increased homeland security spending.
Schieffer also asked Bush when he might officially declare his candidacy.
"Unfortunately, you won't be around for me to announce a possible candidacy," Bush told Schieffer, making note of the moderator's final broadcast after 24 years anchoring the public affairs program.