"He likes the idea of having someone in there with him, and I do, too," Trump told reporters on Thursday when asked if he would ask Pompeo also to replace the hawkish John Bolton, who left on Tuesday.
Trump called Pompeo "fantastic" and said that he gets along with him "so well."
Trump said he was reviewing 15 candidates to take on the "great job" of coordinating US national security.
Media speculation has risen since Bolton's departure that Trump would tap Pompeo -- perhaps in an all-powerful dual role in which he would remain secretary of state.
Such an arrangement is highly unusual but was given to Henry Kissinger by president Richard Nixon as he became embroiled in the Watergate scandal.