Sen. John McCainJohn Sidney McCainRubio asks Army to kick out West Point grad with pro-communist posts The VA's woes cannot be pinned on any singular administration Overnight Defense: Mattis offers support for Iran deal | McCain blocks nominees over Afghanistan strategy | Trump, Tillerson spilt raises new questions about N. Korea policy MORE (R-Ariz.) on Sunday said his colleague, Sen. Tom Coburn (R-Okla.), would be the “best” pick to take over the troubled Veterans Affairs Department.

However, Coburn does not agree.

Just days after Eric Shinseki resigned amid long-running problems at the agency, McCain said Coburn was the right man for the job.

“I'd ask Tom Coburn,” he said on CBS’s “Face the Nation.” “If there's anybody in Congress that knows more about healthcare, then Tom Coburn should be the next secretary.”

Coburn announced in January that he planned to retire from Congress at the end of the year, two years before his term expires. The fiscal hawk has been battling with prostate cancer but said his decision to step down was not due to health reasons.

A spokesman for Coburn said McCain’s remarks were “a very nice compliment,” but that the senator plans to return to private life after he resigns.

McCain seemed to realize he was treading on uncertain ground when he made the remarks.

“I think he’d be the best, and he’s going to kill me for saying that,” he said.

Both McCain and Coburn have argued that the problems at the VA stem far beyond Shinseki and are systemic. McCain argued Sunday that veterans should have more flexibility when it comes to choosing how they get their healthcare, amid long lines at hospitals devoted to their treatment.

“Why should a veteran have to get into a van and ride three hours to get to Phoenix in order to have routine medical care taken care of?” McCain asked. “That's the solution to this problem, this flexibility to the veteran to choose their healthcare, just like other people under other healthcare plans are able to do.”

McCain and Coburn, along with Sen. Richard Burr (R-N.C.), plan to introduce legislation in the coming days that would give veterans more control over where they seek healthcare, according to Coburn’s spokesman.