CNN and Fox are rivals.
The conversation, which was allegedly recorded on March 10, 2016, shows Zucker expressing a familiarity with Trump and Cohen.
"I'm very conscious of not putting too much in email, as you're a lawyer, as you understand. And, you know, as fond as I am of the boss, he also has a tendency, like, you know, if I call him or I email him, he then is capable of going out in his next rally and saying that we just talked and I can't have that, if you know what I'm saying," Zucker said.
"It's not that I don't want to talk to [Trump] every day. I've just got to be careful, because, I've just got to be careful ... I just don't want him talking about it on the campaign trail ... But you know what? I'm going to give him a call right now and I'm going wish him luck in the debate tonight."
Portions of the audio were played during "Tucker Carlson Tonight" on Tuesday.
CNN didn't respond to a request for comment.
Zucker also floated a weekly show, saying it was one of a number of proposals he had to present to Trump.
Zucker told Cohen, who was later arrested and convicted of tax evasion and other charges, that he believed Trump would hold his own in an upcoming debate.
"He's never lost a debate. And you know what? He's good at this," Zucker said, adding later some advice on how to deal with insults that would come from Trump's rivals.
"You know what you should do? Whoever's around him today should just be calling him a conman all day so he's used to it, so that when he hears it from [Marco] Rubio, it doesn't matter. 'Hey conman, hey conman, hey conman.' He thinks that's his name, you know?" he said.
Cohen is scheduled to appear on CNN on Wednesday to promote his new book.
