Former CIA Director David Petraeus wanted GOP presidential candidate Mitt Romney to keep him on if the Republican beat President Obama in last Tuesday's national election, according to Romney associates.

The sources said that Petraeus, who resigned after the election when the White House learned that the married father was caught in a sex affair with his younger, also married, biographer, left open the door to taking another Cabinet post too in pre-election communications with the Romney team.

But the Romney campaign, which was vetting candidates for Cabinet posts in expectation of winning the election, never warmed to putting the highly-decorated retired Army general on their national security team. Campaign associates told Secrets that they were pushing for a Cabinet with no ties to Obama and intelligence officials suggested that the campaign was concerned that Petraeus had politicized the agency in the Benghazi, Libya attack and had let the president take too much credit for the killing of Osama bin Laden, the 9/11 attack mastermind.

"Petraeus allowed Obama to play him like a fiddle," said one Romney campaign advisor. The advisor added: "The Romney team needed their own CIA director. I told them this before Benghazi, and after Benghazi."

The campaign agreed. "They all wanted a fresh team, including Petraeus gone," said the advisor.

Had the sex scandal not killed Petraeus' career and future in Washington, he might have faced other pressures, added another source. That's because the administration was aware of his outreach to Romney officials and were "unhappy."

While reaching out to a competing campaign during a presidential election is unorthodox, it is not unusual that Cabinet officials touch base with campaigns that beat incumbents. Former Clinton CIA Director George Tenet, for example, was kept on by former President George W. Bush, and Bush's dad, George H.W. Bush, sought to stay on in Jimmy Carter's administration.