The Ohio Republican told more than a dozen loyalists during a Capitol Hill lunch meeting that linking a one-year debt-ceiling extension to the reinstatement of cost-of-living benefits, which were reduced in December, would likely gain both liberal and conservative support, two people at the lunch and two others familiar with the session told the newspaper.
President Obama has insisted he will not negotiate over raising the debt ceiling, which is the amount of national debt the Treasury Department can issue to increase the federal government's borrowing authority. Obama has said raising the debt ceiling is a congressional responsibility, not a bargaining chip.
Senate Majority Leader Harry Reid, D-Nev., has also demanded a clean debt-limit increase, with no strings attached.
The borrowing limit is suspended until Friday.
Treasury Secretary Jack Lew has said his department can use extraordinary measures to keep the government borrowing only through the end of the month.
In Wednesday's lunch meeting, Boehner didn't actually endorse the military-benefits debt-ceiling link, the sources told the Post, but said he would talk up the idea with colleagues and urged his allies to do the same.
If the maneuver gains traction, Boehner would consider bringing it to the floor, they said.
"He was very warm to it, seeing it as something that can get us out of this fix," one attendee told the Post.
"I think this could be a way for us to get through the debt ceiling, but the speaker is going to spend the next few days taking the temperature of his members," the attendee said.
House Republican leaders told Boehner earlier Wednesday the GOP's leading options for debt-limit bargaining -- linking an extension to approval of the Keystone XL pipeline or repealing parts of the Affordable Care Act -- had only tepid support, the Post said.
Reid said earlier this week he would like to restore the previous level of cost-of-living benefits for military personnel.
Aides cited by the Post said Reid planned to push legislation as soon as next week to return billions of related funding cut under last year's budget agreement.