Sen. Lindsey Graham of SC, a close Trump confidante, predicted Sessions would be out of his job in the near future, but insisted Trump should wait until after November's midterm elections.
Sessions' original sin in Trump's eyes is that he recused himself from matters connected to the presidential campaign, in which he was a conspicuous cheerleader for Trump - a decision that paved the way for the appointment of special counsel Robert Mueller and the investigation Trump incessantly attacks as a "witch hunt".
The first two Republicans to endorse Mr Trump in the Republican presidential primaries were indicted on separate charges last month, Duncan Hunter, of California, on charges that included spending campaign funds for personal expenses, and Chris Collins, of NY, on insider trading.
Thursday he told the outlet, "I do question what Jeff is doing".
Trump has belittled Sessions in conversations with Republican senators in the past week, Politico reported.
"I view it differently", Trump said.
"I think the immigration issue was poorly handled". Jeff Sessions, then senator, was the third.
Senator Lindsey Graham, who is close to Trump and a defender of Sessions, said last week he believed Trump would appoint a new attorney general but should wait until the elections, in which Republicans are seeking to maintain control of both the House of Representatives and Senate.
Speaking later at a rally in Evansville, Indiana, Trump suggested that the leadership of the Justice Department and Federal Bureau of Investigation were biased against Republicans and that "people are angry".
"There's the belief that if the president taking action with respect to Sessions is going to be an important part of the Mueller obstruction case, most of that case has already been made", one source told Politico.