Representatives of Jared Kushner, President Trump’s son-in-law and senior adviser, have quietly contacted high-powered criminal lawyers about potentially representing him in the wide-ranging investigation into Russia’s influence on the 2016 election, according to three people briefed on the matter.

Some of Mr. Kushner’s allies have raised questions about the link between his current lawyer, Jamie S. Gorelick, and Robert S. Mueller III, the special counsel appointed to investigate the Trump campaign’s ties to Russia, according to one of the people who spoke on condition of anonymity. Before the Justice Department named him to the special counsel post, Mr. Mueller was a law partner with Ms. Gorelick at the Washington firm of WilmerHale.

Such connections are common in Washington legal circles and are often resolved by an acknowledgment from the client of the possible conflict. In this case, Ms. Gorelick urged Mr. Kushner to consider other representation first.

In recent days, Mr. Kushner has had discussions with at least one prominent trial lawyer, one of the people said. And if Mr. Kushner chooses to hire a new lawyer, this person may either supplement or replace Ms. Gorelick’s team.