He will also have a chance to discuss potential bipartisan initiatives, including his $1 trillion infrastructure spending plan.

Mr. Trump has high hopes for his relationship with Capitol Hill. He declared on Friday, just minutes after being sworn in, that “we all want the same thing,” regardless of political party, and, “we’re going to get along.”

Monday’s late-afternoon gathering will be a first test.

Mr. Schumer is slated to be at the Monday meeting with Senators Richard J. Durbin, Democrat of Illinois, Mitch McConnell of Kentucky, the majority leader, and John Cornyn of Texas, the No. 2 Republican; Mr. Ryan; and Representatives Kevin McCarthy of California, the majority leader, Nancy Pelosi of California, the minority leader, and Steny Hoyer of Maryland, the minority whip.

Notably, Mr. Trump is set to meet alone with Mr. Ryan afterward.

Nominees are likely to be only one of the topics.

Senators to introduce bill requiring congressional input if sanctions on Russia are lifted

Mr. Tillerson appears likely to win Senate confirmation, close relationship with President Vladimir V. Putin of Russia and all. But senators are still wary of the Russia connections.

Mr. Schumer and Senator Benjamin L. Cardin of Maryland, the ranking Democrat on the Foreign Relations Committee, are introducing legislation that would require a congressional vote to lift the sanctions that were imposed on Russia after its annexation of Crimea from Ukraine and proxy war in that former Soviet state.

The two senators will emphasize that the legislation will also cover sanctions imposed just weeks ago by Mr. Obama after intelligence agencies concluded that Russia had interfered with the 2016 election in hopes of helping elect Mr. Trump. The measure, modeled after a law that required a congressional vote on the Iran nuclear deal, is expected to have bipartisan support, as that legislation did.