The Times article said Boehner is willing to pass a measure through a combination of Republican and Democratic votes, according to one House Republican.
Following the report, stocks pared their losses. (Click here to track the U.S. stock market.)
(Read more: Boehner to GOP: I won't let the nation default)
Here is the full text of the statement from Spokesperson Michael Steel:
"Speaker Boehner has always said that the United States will not default on its debt, but if we're going to raise the debt limit, we need to deal with the drivers of our debt and deficits. That's why we need a bill with cuts and reforms to get our economy moving again."