By SHANE HARRIS, CAROL E. LEE and JULIAN E. BARNES March 30, 2017

WASHINGTON—Mike Flynn, President Donald Trump’s former national security adviser, has told the Federal Bureau of Investigation and congressional officials investigating the Trump campaign’s potential ties to Russia that he is willing to be interviewed in exchange for a grant of immunity from prosecution, according to officials with knowledge of the matter.

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As an adviser to Mr. Trump’s presidential campaign, and later one of Mr. Trump’s top aides in the White House, Mr. Flynn was privy to some of the most sensitive foreign-policy deliberations of the new administration and was directly involved in discussions about the possible lifting of sanctions on Russia imposed by the Obama administration.

He has made the offer to the FBI and the House and Senate intelligence committees through his lawyer but has so far found no takers, the officials said.

Mr. Flynn’s attorney, Robert Kelner, wouldn’t comment on details of his discussions involving Mr. Flynn, but noted he is a decorated Army veteran with a lifetime of public service.

“General Flynn certainly has a story to tell, and he very much wants to tell it, should the circumstances permit,” Mr. Kelner said.

It wasn’t clear if Mr. Flynn had offered to talk about specific aspects of his time working for Mr. Trump, but the fact that he was seeking immunity suggested Mr. Flynn feels he may be in legal jeopardy following his brief stint as the national security adviser, one official said.

Representatives for the FBI and Senate Intelligence Committee declined to comment. Officials with the House Intelligence Committee didn’t immediately respond to a request for comment.

Mr. Flynn was forced to resign after acknowledging that he misled White House officials about the nature of his phone conversations with the Russian ambassador to the U.S. during the presidential transition.

Mr. Flynn also was paid tens of thousands of dollars by three Russian companies, including the state-sponsored media network RT, for speeches he made shortly before he became a formal adviser to Mr. Trump’s campaign, according to documents obtained by a congressional oversight committee.

At a House Intelligence Committee hearing last week, Democratic lawmakers requested a copy of the security-clearance form that Mr. Flynn was required to file before joining Mr. Trump in the White House, to see if he disclosed sources of foreign income.

And they have asked the Defense Department to investigate whether Mr. Flynn, a retired Army general, violated the Constitution’s emoluments clause by accepting money from RT, which U.S. intelligence officials say is part of a state-funded media apparatus, without authorization, according to a letter several Democratic lawmakers sent Secretary of Defense Jim Mattis in February. CLICK IMAGE BELOW FOR LINK TO VIDEO:

Mr. Flynn’s communications with the Russian ambassador, Sergei Kislyak, have been scrutinized by the FBI, which is examining whether Trump campaign personnel colluded with Russian officials who are alleged to have interfered with the presidential election, according to current and former U.S. officials. Russia has denied the allegations.

Mr. Kelner, Mr. Flynn’s attorney, decried the “unfounded allegations, outrageous claims of treason” and other charges by lawmakers and media commentators.

“No reasonable person, who has the benefit of advice from counsel, would submit to questioning in such a highly politicized, witch-hunt environment without assurances against unfair prosecution,” he said.

Congress and the executive branch have the power to grant immunity from prosecution in exchange for witness testimony or cooperation in an investigation. People granted immunity still can be prosecuted for perjury if they give false information.

Traditionally, investigators grant immunity when they believe a witness’s information is important to the investigation and might not be able to be obtained otherwise. During the investigation of Hillary Clinton’s use of a private email server, the FBI granted limited forms of immunity to some of her aides. Mrs. Clinton wasn’t charged in the matter.

A grant of immunity from Congress would require approval from two-thirds of the congressional committee requesting testimony or a majority vote in the full House or Senate. Congress would then need to notify the attorney general and get the approval of a district court judge.

Mr. Flynn, 58 years old, also has drawn questions about whether he properly disclosed aspects of his work after he left military service.

Earlier this month, Mr. Flynn filed registration forms acknowledging he had previously worked as a foreign agent on behalf of Turkish government interests. The Wall Street Journal reported that while serving as an adviser to the Trump campaign, Mr. Flynn met with top Turkish government ministers and discussed removing a Muslim cleric from the U.S. and taking him to Turkey, according to former Central Intelligence Agency Director James Woolsey, who attended, and others who were briefed on the meeting. The Turkish government has accused the cleric of being behind an attempted coup last year.

A spokesman for Mr. Flynn disputed the account, saying “at no time did Gen. Flynn discuss any illegal actions, nonjudicial physical removal or any other such activities.”

Mr. Flynn is one of at least four people associated with the Trump campaign who are part of a wide-ranging counterintelligence investigation by the FBI, according to the current and former U.S. officials.

The other three—former Trump campaign manager Paul Manafort and former Trump advisers Roger Stone and Carter Page—all have volunteered to speak to the House and Senate committees and haven’t asked for immunity from prosecution, according to the individuals, committee officials and representatives for the individuals.

—Aruna Viswanatha and Byron Tau contributed to this article.

Write to Shane Harris at shane.harris@wsj.com, Carol E. Lee at carol.lee@wsj.com and Julian E. Barnes at julian.barnes@wsj.com