The task may be harder than it seems given the hacks occurred so many years ago, said Scott Kessler, deputy global director and industry analyst at CFRA Research. Public behavior toward the company hadn't changed because of the leaks, he pointed out.
"The usage of a lot of their major offerings didn't seemingly get negatively affected by these revelations," Kessler said.
Verizon may consider asking for a price cut on its initial $4.8 billion offer for the company or consider scrapping the deal all together due to the news that a data breach in August 2013 affected more than 1 billion accounts, according to Bloomberg.
Yahoo said it was unrelated to the 2014 breach which leaked information about 500 million user accounts, which was announced in September.
The company did not provide any information on changes on user behavior because of the latest incident. However, Yahoo reported in October as part of its third-quarter earnings report that user engagement trends — which is a measure of website traffic that advertising prices are determined from — was very minimally affected, if even at all, after it revealed information about the 2014 leaks.
User engagement includes page views on Yahoo properties, mail read and sent, searches, and page views on main verticals.
"It doesn't seem like that much of an impact on its user base," Kessler added. "That's a big part of what Verizon has been focused on and buying into. So, I think it's going to be hard to make an argument that there was an material adverse change when usage didn't change at all."
However, part of Yahoo's valuation involves user information it can provide in the future to Verizon's business, said Forrester principal analyst Jeff Pollard. And, consumer confidence in the company is absolutely affected going forward, not to mention businesses that may have considered using Yahoo services, he added.
"Imagine the next time that you are at a log-in prompt, and you are about to sign up for a Yahoo service," Pollard said.
"You'll think, 'But wait a second, I can't give my email. They obviously don't care about it.' Verizon isn't buying Yahoo just based on Yahoo now. Verizon is buying Yahoo based on 2017 and 2018 (and onward). I don't think Yahoo can make a bold statement that this can't affect them in the future."
"As we've said all along, we will evaluate the situation as Yahoo continues its investigation," a Verizon spokesperson told CNBC, declining to comment further. "We will review the impact of this new development before reaching any final conclusions."
"We are confident in Yahoo's value and we continue to work towards integration with Verizon," a Yahoo spokesperson told CNBC.
It's more likely that Verizon will aim to negotiate a lower price for Yahoo, Kessler said. The company still has value for Verizon's plans to become a media and digital advertising powerhouse, especially when coupled with AOL's capabilities.
"I absolutely think there's still an appetite for these brand properties," said Kessler. "Yahoo has a strong franchise across other content areas, not just email and messaging."
Yahoo is still expected to take in $2.98 billion in digital ad revenue globally in 2016, or about 1.5 percent of the worldwide budget, according to eMarketer. It comes in seventh overall, behind Google, Facebook, Alibaba, Baidu, Tencent and Microsoft.