Lugar, a Republican, told ABC television's "This Week" programme on Sunday that talks with Iran could prove "useful" in breaking the impasse.
He said: "Now, the Iranians are a part of the energy picture. Clearly their ties with India and with China, quite apart from others, are really critical.
"We need to talk about that."
He suggested that discussions on Iran's nuclear programme could be held alongside future talks about Iraq.
Appearing on the same programme Evan Bayh, a Democratic senator, agreed that direct talks with Iran could lead to a breakthrough - but added a caveat.
Bayh said: "I don't think there's anything to be lost by opening a dialogue with them.
"But I don't think we should have any illusions either.
"The Iranians are hardened people. They've made a strategic decision that they want to acquire nuclear weapons. I don't think they will respond to words alone.
"I think we need to pursue them as best we can to show them that there will be a price to be paid if they continue to go down the nuclear path."
Any direct meeting would mark a break in an almost three-decade pause in open bilateral relations between US and Iranian officials after the country's 1979 Islamic revolution.
But tensions are running high with the United States pushing for tough UN Security Council action over Iran's disputed nuclear programme.