His comments on ABC's "This Week" came after some had mentioned the secretary of state as a possible replacement for retiring Justice John Paul Stevens.
The former president urged President Barack Obama to pick a nominee from the political arena, noting justices often used to come from politics, though all nine now on the high court came from the federal bench.
"I hope he'll take a look at somebody who hasn't been a judge," Clinton said. "Some of the best justices in the Supreme Court in history have been non-judges, people that, as (the late justice) Hugo Black once famously said, had been sheriffs and county judges, people that have seen how the lofty decisions of the Supreme Court affect the ordinary lives of Americans."
He said Obama should seek a nominee in the late 40s or early 50s and added neither he nor his wife has any interest in becoming a justice.
"I think at one point in her life she have might been interested in it," he said. "But she's like me, you know. We're kind of doers. We like being out there and doing things, rowing our own boat and making changes we could see happen."
As president, Clinton nominated Justices Ruth Bader Ginsburg and Steven Breyer to the Supreme Court.
He said he had failed in his efforts to persuade then-New York Gov. Mario Cuomo and then-Senate Majority Leader George Mitchell to agree to be nominated to the high court.