New York (CNN Business) Fox News hosts and personalities have been instructed over the last several days not to identify the whistleblower whose complaint sparked an impeachment probe against President Trump, people familiar with the matter told CNN Business.

Several hosts and commentators on the network who have been supportive of President Trump seem to want to name the person they believe to be the whistleblower, but Fox's guidelines have said not to do so.

JUST WATCHED Jeffrey Toobin: Yes, unmasking a whistleblower is illegal Replay More Videos ... MUST WATCH Jeffrey Toobin: Yes, unmasking a whistleblower is illegal 02:39

Right-wing media hyped a report from a website last week which claimed it had likely identified the possible whistleblower. Fox is perhaps the only major component of the right-wing media machine that has, thus far, refrained from naming the person identified by that story.

No mainstream news organization has identified the whistleblower. CNN has sent guidance to staff about not repeating any reporting that alleges the name and identity of the whistleblower.

It's possible that the situation at Fox could change if there were to be a development in the story or if Trump himself names a person he believes to be the whistleblower.

Read More