WASHINGTON — American spies collected information last summer revealing that senior Russian intelligence and political officials were discussing how to exert influence over Donald J. Trump through his advisers, according to three current and former American officials familiar with the intelligence.

The conversations focused on Paul Manafort, the Trump campaign chairman at the time, and Michael T. Flynn, a retired general who was advising Mr. Trump, the officials said. Both men had indirect ties to Russian officials, who appeared confident that each could be used to help shape Mr. Trump’s opinions on Russia.

Some Russians boasted about how well they knew Mr. Flynn. Others discussed leveraging their ties to Viktor F. Yanukovych, the deposed president of Ukraine living in exile in Russia, who at one time had worked closely with Mr. Manafort.

The intelligence was among the clues — which also included information about direct communications between Mr. Trump’s advisers and Russian officials — that American officials received last year as they began investigating Russian attempts to disrupt the election and whether any of Mr. Trump’s associates were assisting Moscow in the effort. Details of the conversations, some of which have not been previously reported, add to an increasing understanding of the alarm inside the American government last year about the Russian disruption campaign.