Adding to a debate that is beginning to brew in earnest in the lame duck session of Congress in Washington, Conrad said, "I would go for changing the tax system fundamentally. And I'd have an extension (of the tax cuts) until that was accomplished," The Wall Street Journal reported Wednesday.
The fundamental breakdown of the debate has been Republicans favoring an extension of all the Bush-era tax breaks, including breaks for individuals earning over $200,000 or families with a net income over $250,000.
President Barack Obama favors the extension for all but the wealthiest taxpayers.
Conrad made his comments at an event sponsored by the Peter G. Peterson Foundation in Washington. The group advocates for deficit reduction, the Journal said.
At the event, Sen. Evan Bayh, D-Ind., took a similar stance, but tied his vision of a tax overhaul to deficit reduction.
"For the next couple of years we need to err on the side of growth … but after that we need to quickly pivot and begin reducing this debt," he said.