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.