His latest comment, made in an interview with The Associated Press, was a reversal of his earlier remark that he would not comply with Mueller's subpoena but would instead risk arrest.
Nunberg told the AP that he's angry about being asked to share his communications with a long list of people. He added that he doesn't think the subpoena is fair and that Mueller's team should narrow its scope of inquiry.
However, he conceded that he would "end up cooperating" with Mueller.
The special counsel's subpoena had asked Nunberg to hand over communications related to Trump and nine other people, and to appear in front of a grand jury investigating whether Russia interfered in the U.S. 2016 presidential election.
In a series of disjointed interviews late Monday in the United States, Nunberg said he thinks the special counsel might have something on the president.
When asked whether Mueller's team could have something, Nunberg told MSNBC, "I think they may."
Nunberg's bombshell came during a media blitz Monday as he told various outlets that he would refuse to comply with Mueller's subpoena in the Russia probe.
Nunberg, who was an advisor on Trump's presidential campaign, told MSNBC that it would be "really funny" if Mueller arrested him for ignoring the grand jury subpoena. Laughing, he said that "my lawyer is about to dump me right now."
Mueller is investigating possible collusion between the Kremlin and the Trump campaign during the 2016 campaign. The probe has picked up momentum in recent weeks, yielding indictments of 13 Russians accused of waging "information warfare" to swing the election to Trump, and a guilty plea from former top Trump campaign official Rick Gates.
Trump has repeatedly denied allegations of collusion.
Nunberg told MSNBC that investigators have been asking, "Did you hear people speaking Russian in the Trump office?" and "Did you hear about Trump Tower Moscow?"
He said he had not heard Russian being spoken in the office, calling the question "ridiculous."
Trump's company reportedly sought a deal to build a Trump Tower in Moscow while he was running for president. The project never came to fruition.
Nunberg also claimed that Mueller's team told him "flat-out" that Trump was taking positions on different policies because of his business interests. Nunberg strongly denied that Trump ever said that he made policy decisions based on his businesses.
The MSNBC interview came after The Washington Post published a story that cited Nunberg as saying he would refuse to comply with the subpoena. "Let him arrest me," Nunberg told the newspaper. "Mr. Mueller should understand I am not going in on Friday."
Nunberg said that he was refusing the special counsel "because what they sent me was absolutely ridiculous."
"Should I spend 50 hours going over all my emails with [Trump confidant and longtime political operative Roger Stone] and with Steve Bannon?" Nunberg said in the MSNBC interview, adding that Mueller's team also asked for communications with former Trump campaign staffers Hope Hicks and Corey Lewandowski. Last week, the White House said Hicks, a longtime close aide to Trump, would be leaving her role as communications director.
Despite being "not a fan of Donald Trump" for the way Nunberg says he treated Stone and others, the former Trump aide said that "when they get a subpoena like this ... Mr. Trump's right, it's a witch hunt."
But when asked whether he believed that the special counsel may have something on Trump, Nunberg responded, "I think they may."
He added: "I think that he may have done something during the election. But I don't know that for sure."
Nunberg softened his stance somewhat in a later interview with CNN.
"I suspect that they suspect something about him," he told the network in an interview. "I can't explain it unless you were in there. ... The way they asked about his business dealings, the way they asked if you heard anything even while I was fired ... it just made me suspect that they suspect something about him."
CNN also asked whether investigators sought information about plans for a Trump Tower Moscow. "Yes," Nunberg said.
In a later CNN interview on Monday, Nunberg alleged that Trump knew about the now-infamous June 2016 meeting between Trump campaign officials — including Donald Trump Jr., Paul Manafort and Jared Kushner — and reportedly Kremlin-connected Russians, who promised damaging opposition research on then-candidate Hillary Clinton.
"He talked about it a week before," Nunberg said of Trump. "All he had to say was, 'Yeah, we met with the Russians. The Russians offered us something, and we thought they had something and that was it.' I don't know why he went around trying to hide."
White House staff initially denied the meeting involved the president in any way, but a Washington Post report later alleged that Trump was directly involved in crafting the initial, misleading statement claiming that the meeting was centered around Russian adoption.
The Associated Press reported in December 2017 that Trump Jr. testified before the Senate Intelligence Committee that he had not told his father about the meeting at the time it happened.
White House press secretary Sarah Huckabee Sanders on Monday said that Nunberg is "incorrect" in saying Mueller could have something on Trump.
"As we've said many times before, there was no collusion with the Trump campaign," Sanders said. "Anything further on what his actions are, he hasn't worked at the White House so I certainly can't speak to him or the lack of knowledge that he clearly has."
Nunberg was a top advisor to Trump even before the real estate magnate's presidential campaign officially began. He advised Trump during his flirtation with running for president in 2012. A February 2014 Buzzfeed article about Trump's presidential ambitions referred to Nunberg as "Trump's political right hand."
Nunberg worked as a Trump campaign aide until August 2015, when he was fired after reports emerged of racially charged Facebook posts that he allegedly wrote. At the time, Nunberg denied he wrote the posts, which involved the use of racial and religious slurs against then-President Barack Obama and Rev. Al Sharpton.
Nunberg and Trump sued each other in 2016. Trump accused Nunberg of leaking dirt to the New York Post, while Nunberg alleged that Trump might have broken campaign finance laws. Trump and Nunberg settled their legal dispute later that year.
The White House did not immediately respond to CNBC's request for comment.
— CNBC's Christina Wilkie contributed to this report.