They were uncertain he could overcome doubts raised by his conviction for mishandling classified information and win confirmation to be secretary of state if he is picked by President-elect Donald Trump. Some were worried it could spark a major confirmation battle in the opening weeks of the Trump administration.
One GOP senator said there is a "a high level of angst" among Republican senators about the political fallout if Petraeus were to be chosen.
"I have had discussions with several of my colleagues who have expressed anxieties about this issue because, after all, this was an issue in the campaign for Hillary (Clinton) and this individual was actually convicted. It's surprising to us that he's in the mix," said the senator who agreed to speak candidly if not identified.
Another Republican senator privately echoed those concerns saying the choice of Petraeus, who was convicted of giving classified materials to his biographer
with whom he was having an extra-marital affair, would be a "self-made fight" and give "pause" to many Republicans.
A third Republican senator, who spoke highly of Petraeus, acknowledged, "it obviously will provoke a lot a discussion."
"But if that's what the President-elect wants to do and Petraeus is willing to go through it, I assume he gets confirmed," that same senator said.
Sen. Jeff Flake of Arizona, a Republican on the Foreign Relations Committee, which would hold confirmation hearings for the position, refused to say if Petraeus could easily be confirmed.
"Let's wait for the real nominee," Flake said.
Several other senators defended the decorated and celebrated general, predicting he would be confirmed with support from Republicans and Democrats.
Arizona Sen. John McCain, a vocal Republican supporter, said he didn't think the conviction would prevent Petraeus from getting his security clearance back or winning confirmation.
"I am confident of that, yes. Because of his reputation and the fact is he was convicted of a misdemeanor, paid his penalty for his crime and we move on in life," said McCain, who chairs the Armed Services Committee.
"Petraeus is highly regarded on both sides of the aisle. In fact, some people were alleging, it may be true I don't know, that he was closer to Clinton than he was to the Republicans. They served together in the cabinet and all that," McCain said. "I haven't taken a poll or counted votes but I know how highly regarded he is."
One senior Republican aide noted a fight over Petraeus could be damaging for Democrats since they seemed to forgive Democratic Presidential nominee Hillary Clinton of her misuse of a private email server while secretary of state.
The top Democrat on the Intelligence committee, Sen. Dianne Feinstein of California, was asked by CNN Tuesday if Petraeus conviction was disqualifying and replied, "I'm not going to make that judgment right now."
She praised the general's extensive military resume and said "I've got to think about it."
One former Republican senator, who remains very plugged into the caucus, said GOP senators see there are obvious political problems with Petraeus and other top contenders on Trump's list, including Rudy Giuliani and Mitt Romney. He said the GOP senators he's talking to keep coming back to Sen. Bob Corker of Tennessee, who is chairman of the Foreign Relations Committee, as the best choice for the job.
A reflection of the GOP unease came from another former senator. Richard Lugar, of Indiana, who for years was the respected top Republican on the Foreign Relations Committee, was back in the Capitol Thursday for an event.
Asked by CNN if he was comfortable with Trump's short list to be secretary of state, Lugar said bluntly, "no."
Asked who he was uncomfortable with, Lugar responded with a nervous laugh, "Well, I'm not going to tell you."