Mr Coats, 76, had disagreements with the president over Russia, Iran, North Korea, and Brexit.
Mr Trump was said to be considering replacing him with John Ratcliffe, a Republican congressman who has been a staunch loyalist, according to the New York Times.
Mr Ratcliffe sits on the House judiciary committee, and Mr Trump was said to have been impressed by his recent aggressive questioning of special counsel Robert Mueller.
Mr Coats, who was appointed by Mr Trump, has served in the role since March 2017.
He clashed with Mr Trump early on, taking a hard line toward Russia that sharply contrasted with the conciliatory approach the president pursued with Vladimir Putin, the Russian president.
Earlier this year Mr Coats told Congress that North Korea was unlikely to give up its nuclear weapons, contradicting Mr Trump’s statement that Pyongyang no longer posed a threat.
He also told Congress that Iran had continued to comply with a nuclear deal that Trump abandoned.
Mr Coats, a former Republican senator, served in Mr Trump’s cabinet.
He was previously US ambassador to Germany under George W Bush.
The role he holds was created after the September 11, 2001 terror attacks, and he has overseen the work of America’s 17 intelligence agencies.