Political strategist Paul Manafort stepped out of the limelight last summer, resigning as Donald Trump’s campaign manager in August after his connections to pro-Russia tycoons drew controversy.

Within days, Mr. Manafort resumed advising Mr. Trump privately on navigating the Washington establishment and other questions, and in recent months he expressed interest in a potential business arrangement with a major Trump donor and fundraiser, people familiar with the matter say.

Now the ties that drove Mr. Manafort from the campaign have become liabilities again, as he sits at the center of high-profile investigations into alleged links between Moscow and people in President Trump’s orbit.

The Senate Intelligence Committee is looking into any possible collusion between Russia and people linked to Mr. Trump, top senators have said. The activities of Mr. Manafort and others are under scrutiny because of their ties to Russian interests, people familiar with the matter have told The Wall Street Journal. The Russian connections have come into greater focus since last week’s resignation of National Security Adviser Mike Flynn over his discussions in December about U.S. sanctions with the Russian ambassador, which he initially denied having.

Mr. Manafort’s conversations with Mr. Trump after he left the campaign included discussion of an opposition research dossier related to Russia that was published online in January, a person familiar with the matter said.