Of course he can. This was in a leaked memo saying that the President can target people if they are linked to terrorism goes outside the court of a trail. Now is it legal and fair. Well those are two separate questions. When we invaded Iraq. Was it fair was targeted people locking them in a supermax like prison and torturing them for hours on end without allowing them due access to due process.
Of course that shouldn't been legal. The superme court said three times while Bush was President. You cannot just grab someone throwing them in a jail without evidence of any kind. But we did it anyways. Now we use drones to soar through the sky killing people and innocent bystanders. Again not prolly legal or fair. In fact most likely in violation of international law the first two. But we did it anyways.
Now only when An American is killed without due process do we only blink and wonder if this is legal. Most of it is likely stuff we're making up as we go along. However they are the Gov and we are the people. We cannot really do anything about it. 9/11 was a game changer that truly changed the core of America and how we respond to attacks. It's not a simple yes or no answer.
Oh no. It's more complex then that. But that's my answer.