President Trump's attorney Rudy Giuliani said Sunday that his client did not have to comply with a potential subpoena from special counsel Robert Mueller in the Russia investigation.

"He's the president of the United States," Giuliani told ABC News' "This Week." He continued, "We can assert the same privilege as other presidents have. President Clinton negotiated a deal in which he didn't admit the effectiveness of the subpoena. [Independent Counsel Kenneth Starr] withdrew it."

In the wide-ranging interview, Giuliani also addressed the investigation into Trump's personal attorney Michael Cohen, saying Cohen may have paid off other woman accusing the president of misconduct aside from adult-film star Stormy Daniels: "I have no knowledge of that, but I would think if it was necessary, yes."

When asked if Trump would be willing to testify before a grand jury in the Russia investigation, Giuliani said he was looking for "the Hillary Clinton treatment," a reference to the FBI's interview of the former secretary of state during the investigation into her personal email server.

"That is no [questioning] under oath, only a Q&A, and then we get the questions in advance, and they write the report two weeks before," Giuliani said.

Giuliani also reiterated that he was unwilling to allow Trump to be interviewed by Mueller, despite the president's reported openness to the idea -- and refused to rule out Trump asserting his Fifth Amendment right against self-incrimination.

"They don't have a case on collusion. They don't have a case on obstruction, which is why they're asking all these cockamamie questions about what do you feel, what do you think," Giuliani said. "I'm going to walk him into a prosecution for perjury like Martha Stewart did?"

Giuliani was referencing the lifestyle maven convicted in 2004 of lying to investigators and obstruction in an insider-trading case.

Giuliani told Fox News' Sean Hannity on Wednesday that Trump had reimbursed his personal attorney, Michael Cohen, for a $130,000 payment made to Stormy Daniels in the closing days of the 2016 election campaign. Daniels has sued to invalidate a nondisclosure agreement about an alleged sexual encounter with the married Trump in 2006.

When asked Sunday whether Trump knew about the payment to Daniels after the campaign, Giuliani demurred.

"I can't prove that. I can just say it's rumor," Giuliani said.

Cohen "made payments for the president, or he conducted business for the president," Giuliani said, "which means he had legal fees, monies laid out, and expenditures, which I have on my bills to my clients."

Cohen no longer represents Trump, Giuliani said, adding that it would "be a conflict right now." Cohen faces a criminal investigation in New York, where FBI agents raided his home and office several weeks ago seeking records about the Daniels nondisclosure agreement and other matters.

Michael Avenatti, Daniels' attorney, said Sunday on "This Week" that he thinks it's "obvious ... to the American people that this is a cover-up, that they are making it up as they go along."

Both Giuliani and Trump have insisted the payment to Daniels was not a campaign expense.

Giuliani maintained Sunday that the payment could not be considered an in-kind campaign contribution because there was another explanation for it.

"This was for another purpose, to protect him, to protect his family," he said. "It may have involved the campaign. Doesn't matter."

Giuliani said the financial arrangement with Cohen wasn't revealed on Trump's 2017 personal financial disclosure because "it isn't a liability, it's an expense."