A White House official said Obama invited Ryan and U.S. Rep. Chris Van Hollen, D-Md., the ranking Democrat on the Budget Committee to lunch Thursday, The Wall Street Journal reported.
The lunch is the latest sign that Obama is trying to restart discussions with Republicans to produce a "grand bargain'' on deficit-cutting, as well as reforms to entitlement programs and the tax code.
Ryan is the architect of the House Republican plan to corral federal spending and reform the Medicare program. He's scheduled to next week release the House GOP's version of a budget for the next fiscal year.
Ryan said Wednesday that his proposal would be similar to his last blueprint and would contain no "big surprises," The Hill reported.
His proposal last year would have cut $5 trillion in spending and balanced the budget by 2040. This year, Ryan pledged to conservative House members that his proposal that would balance the budget by 2023.
Obama began calling GOP senators last weekend, focusing on lawmakers outside the Senate leadership.
On Wednesday, Obama ate dinner with a dozen Senate Republicans at a Washington hotel, where the conversation topics included taxes and spending, participants said.
White House officials and other familiar with the discussions told the Journal Obama's aim is to reach out beyond congressional Republican leaders to build a coalition that will pass a budget package that would reduce the deficit, raise tax revenue, rework the tax code and buttress Social Security and Medicare.
The White House said Obama and the 12 GOP senators had a "good exchange of ideas."
U.S. Sen. Mike Johanns, R-Neb., appeared to agree, telling ABC News: "His goal is ours. We want to stop careening from crisis to crisis ... solving every problem by meeting the crisis deadline. Today was a good step and we'll see what happens."
The dinner at the Jefferson Hotel near the White House came five days after the automatic, across-the-board spending cuts of $85 billion, known as the sequester, took effect.
Besides Johanns, Republicans attending the dinner included Lindsey Graham of South Carolina, Bob Corker of Tennessee, Kelly Ayotte of New Hampshire, John McCain of Arizona, Dan Coats of Indiana, Tom Coburn of Oklahoma, Richard Burr of North Carolina, Pat Toomey of Pennsylvania, Ron Johnson of Wisconsin, John Hoeven of North Dakota and Saxby Chambliss of Georgia.