WASHINGTON — President Trump is strongly considering nominating William P. Barr, who served as attorney general during the first Bush administration from 1991 to 1993, to return for a second stint as head of the Justice Department, according to people close to Mr. Trump.

Mr. Barr, a Republican and corporate lawyer, has long advanced a vision of sweeping presidential powers. Mr. Trump’s growing focus on him comes amid a rocky reception for Matthew G. Whitaker, whom the president installed last month as acting attorney general after ousting Jeff Sessions from the post.

With Democrats vowing oversight hearings into Mr. Whitaker when they take over the House in January, the president is said to be under pressure — including from allies like Republican senators Charles E. Grassley of Iowa and Lindsey Graham of South Carolina, the departing and incoming chairmen of the Senate Judiciary Committee — to quickly nominate a viable successor to Mr. Sessions.

Mr. Barr is seen as the leading candidate for the nomination if Mr. Trump does not decide to stay with Mr. Whitaker for an extended period, several Justice Department officials said this week. And while Mr. Trump is known for changing his mind capriciously, he likes to poll advisers and confidants about potential nominees and has asked several people about Mr. Barr recently.