President Trump believes the chances that witnesses will be called at his impeachment trial in the Senate have grown, even as advisers believed they might be able to allay concerns from senators after reports about assertions made by his former national security adviser, John R. Bolton, in an unpublished manuscript.

According to several people who spoke to him, Mr. Trump has sounded resigned to the possibility of witnesses after The New York Times reported Sunday that Mr. Bolton’s manuscript described the president directly tying the release of security aid to Ukraine to the country’s pursuit of investigations he sought into Democrats.