President Donald Trump is considering naming embattled Attorney General Jeff Session to lead the Department of Homeland Security, according to reports.

Sessions has been the target of unprecedented public criticism in recent weeks with the president saying he was "very disappointed" in the former Alabama Senator and long-time Trump supporter for recusing himself from an investigation into Russian interference in the 2016 election. Trump has not said if he has still has confidence in the Attorney General while Sessions insists he has no plans to resign.

"If he wants to make a change he can certainly do so," Sessions said. "I would be glad to yield in that circumstance, no doubt about it, but I do believe that we are making tremendous progress."

Trump is reportedly considering moving Sessions to head the Department of Homeland Security, a vacancy created last week when retired Gen. John Kelly was named the new White House chief of staff after the ouster of Reince Priebus. A new AG could pave the way for the president to tap an attorney general who could take over the investigation into Russian interference from special counselor Robert Mueller.

The change would also put Sessions at the head of an agency leading up Trump's immigration efforts, a key issue for the AG as a Senator.

That doesn't mean it's a popular idea, however. Sen. Lindsey Graham, R-Ky., tweeted:

AG Jeff Sessions has a good ring to it.



Highly qualified, committed to the rule of law, tough on crime, and fiercely independent. (1/2) https://t.co/nwt2pi1iYc — Lindsey Graham (@LindseyGrahamSC) July 29, 2017

DHS Secretary Jeff Sessions doesn't sound right, doesn't feel right.



Bad idea. (2/2) https://t.co/nwt2phJHzC — Lindsey Graham (@LindseyGrahamSC) July 29, 2017

Other names under considering, according to Politico, include Texas Rep. Michael McCaul, chairman of the House Homeland Security Committee; Thomas Homan, acting director of U.S. Immigration and Customs Enforcement; and Kansas Secretary of State Kris Kobach, who is leading up the president's commission on voter fraud.