Former Sen. Rick Santorum (R-Pa.) said Sunday that President TrumpDonald John TrumpDem lawmaker says Electoral College was 'conceived' as way to perpetuate slavery Stanley Cup champion Washington Capitals to visit White House on Monday Transportation Dept requests formal audit of Boeing 737 Max certification MORE's next chief of staff should be someone with more of a political background than John KellyJohn Francis KellyMORE had in his roughly 17 months in the role.

"I think the lockdown tough general that Trump respects didn't work, didn't work in controlling Trump," Santorum, a political analyst for CNN, said on "State of the Union."

"I like the idea of someone who is a politician, someone who is respected by the president for his political instincts," he continued. "Because that, to me, is sort of the secret sauce of how you get the president to focus more on his agenda and the things many of us have been telling him to focus on."

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Santorum made a point to say he is not interested in being Trump's chief of staff.

The former senator suggested that Nick Ayers, who is currently Vice President Pence's staff and considered a front-runner to replace Kelly, is someone who would have the necessary background to push through Trump's agenda.

Trump announced as he left on Saturday for the Army-Navy football game that Kelly would depart as chief of staff by the end of the year. The announcement followed months of reporting that detailed an acrimonious relationship between the two men and predicted Kelly's ouster was imminent.

Kelly, a retired Marine Corps general, joined the Trump administration in January 2017 as secretary of Homeland Security, and moved over to chief of staff in the summer of 2017. He was Trump's second chief of staff, after Reince PriebusReinhold (Reince) Richard PriebusMulvaney poised to become permanent White House chief of staff: report DNC decision to shut out Fox News hurts Democratic candidates and Americans The five Trump communications directors who have come and gone MORE.