WASHINGTON — In the nearly two years that the special counsel, Robert S. Mueller III, has been investigating whether there was collusion between Russia and the Trump campaign, few figures seem to have offered more tantalizing leads than Konstantin V. Kilimnik.

A diminutive, multilingual political operative who was born in Ukraine while it was still part of the Soviet Union, Mr. Kilimnik has continued to attract intense interest from prosecutors for his interactions with his longtime boss and mentor, Paul Manafort, and his suspected ties to Russian intelligence, even as Mr. Mueller prepares to wrap up his investigation.

The full story of what Mr. Mueller has found about cooperation between the Trump campaign and Russia during the 2016 presidential election is not known. But Mr. Kilimnik pops up repeatedly as a possible connection, with ties to both sides that are as enigmatic as they are deep.

And his dealings with Mr. Manafort, who in 2016 served as Donald J. Trump’s campaign chairman, encompass two of the most intriguing elements of the special counsel’s inquiry to surface publicly: the sharing of polling data with Mr. Kilimnik, and the work he and Mr. Manafort did on behalf of Kremlin-aligned Ukrainian interests that were pushing plans that could have eased economic sanctions imposed on Russia by the United States and its allies.