The arrest of the former agent, Jerry Chun Shing Lee, 53, capped an intense F.B.I. investigation that began around 2012 after the C.I.A. began losing its agents in China.
President Trump has offered lavish praise when the intelligence community or law enforcement investigates his opponents but rebuked them when their actions do not align with his interests.
The views of Mike Pompeo, the C.I.A. director, have put him in good stead with President Trump, who has come to value his pungent opinions and hard-charging style.
Mr. Cotton, a senator from Arkansas, would be the youngest person ever to run the C.I.A. should a White House plan to shuffle the cabinet come to fruition.
A transition plan developed by John F. Kelly, the White House chief of staff, would install Mike Pompeo, the C.I.A. director, as secretary of state, officials said.
Ahmed Abu Khattala was the first person charged and prosecuted in the attacks in Benghazi, Libya, which left four Americans dead, including an ambassador.