(CNN) National Security Adviser Robert O'Brien said he's spoken in the past few days with Secretary of State Mike Pompeo, who told him he's not running for a US Senate seat in Kansas.

"I hope and I expect Secretary Pompeo will stay. I spoke with him about this two nights ago. He said he's not running for Senate. He said he's staying as secretary of state," O'Brien said Sunday on ABC's "This Week."

Speculation has mounted that Pompeo may be preparing to leave his post to mount a run for Senate, fueled partly by the creation of new social media accounts casting the hard-nosed diplomat in a softer light.

Some Trump administration officials have been tossing around names for potential replacements, sources told CNN last week. They included O'Brien, as well as Treasury Secretary Steven Mnuchin and Deputy Secretary of State Stephen Biegun.

O'Brien said Sunday he "loves" the job he currently holds. "I'm happy sitting where I am," he said.

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