The Senate might look at tweaking its Wall Street reform bill from last year, but not repealing it, Sen. Mark Warner (D-Va.) said Thursday.

Warner, a member of the Senate Banking Committee who'd been a key negotiator of last year's financial regulatory reform legislation — the "Dodd-Frank" bill — rejected the possibility of repealing it, as a bill in the new Republican House has sought.

"If there are ways that we can tweak it here or there, but I don't think overall repeal of Dodd-Frank," Warner said Thursday on CNBC.

Rep. Michele Bachmann (R-Minn.), a member of the House Financial Services Committee, introduced legislation last week seeking to do away with the legislation, which was one of the more popular accomplishments of the past two years of Congress.

It's unclear whether that bill will advance through the House, but if it succeeds, it will likely meet authorization in the Democratic-controlled Senate.

Still, Warner indicated the possibility of changes to the bill, striking a similar tone as some centrist Democrats have with healthcare — indicating a greater flexibility in the party's legislative strategy.

"After that bill came through, I felt pretty good about it, because we got an equal amount of criticism from the left that the bill didn't go far enough as we did from the right that the bill went too far," Warner said. "So if I'm getting incoming from both sides, we may have struck the right balance."

The Virginia centrist added: "There is a lot in the bill that still has to be worked out by the regulators. But I think we in this country are actually ahead of our Asian and European counterparts, in terms of shoring up the stability of our banking industry."