Verizon is pushing for a $1 billion discount off its pending $4.8 billion agreement to buy Yahoo, several sources told The Post exclusively.

The request comes on the heels of the web giant getting bludgeoned by bad news in the past few days.

Yahoo revealed two weeks ago that it had been hacked in 2014 and that usernames and passwords for 500 million accounts were swiped.

Then, earlier this week, it was learned that Yahoo had been ordered by a secret Foreign Intelligence Surveillance Court to scan emails for terrorist signatures.

“In the last day we’ve heard that [AOL boss] Tim [Armstong] is getting cold feet. He’s pretty upset about the lack of disclosure and he’s saying, ‘Can we get out of this or can we reduce the price?’” said a source familiar with Verizon’s thinking.

That might just be tough talk to get Yahoo to roll back the price. Verizon had been planning to couple Yahoo with its AOL unit to give it enough scale to be a third force to compete with Google and Facebook for digital ad dollars.

The discount is being pushed because it feels Yahoo’s value has been diminished, sources said.

AOL/Yahoo will reach about 1 billion consumers if the deal closes in the first quarter, with a stated goal to reach 2 billion by 2020. Armstrong flew to the West Coast in the past few days to meet with Yahoo executives to hammer out a case for a price reduction, a source said.

“Tim was out there this week laying the law down and [Yahoo CEO] Marissa [Mayer] is trying to protect shareholders,” said a source close to talks. “Tim knows how to be fair, while Verizon is pushing him, he can bridge the gap.”

At the same time, the Yahoo deal team is pushing back hard against any attempts to negotiate the price down, sources said.

Yahoo is telling Verizon that a deal is a deal and that the telecom giant has no legal avenue to change the terms. Yahoo’s next board meeting is in two weeks but the two parties are continuing discussions.

The setbacks, however, aren’t helping AOL, which hasn’t completed integrating itself with Verizon, which acquired it 16 months ago for $4.4 billion.

Armstrong’s push for a $1 billion discount on the price is, one person told The Post, on top of a $1 billion reserve that Verizon may set aside to fund possible liabilities associated with the Yahoo email hack.

“They’re being cautious because they don’t know what they’re going to find,” the person said.

Former acting CEO Ross Levinsohn told CNBC on Wednesday, “If I’m sitting at Verizon right now … just from a business standpoint, I’d probably reserve a bunch of money against the deal or go back to Yahoo and ask for a discount.”

Yahoo and Verizon declined comment.

Yahoo shares closed Thursday down 3 cents, to $43.68, while Verizon shares closed unchanged at $50.26.