NEW YORK (CNNMoney) -- The long drama between Yahoo and Verizon may finally be coming to an end.

Yahoo's stock popped more than 2% in early trading Wednesday following reports Verizon may only ask for a slight price cut in its deal to buy the Internet company.

Verizon is said to be close to finalizing an amended deal with Yahoo that could shave $250 million to $300 million off the original $4.83 billion price tag, according to reports from Bloomberg and The Wall Street Journal.

Reps for Yahoo and Verizon declined to comment on the reports.

The agreement would be welcome relief to Yahoo investors. There have been doubts about the deal for months as a result of Yahoo revealing not one, but two massive security breaches affecting more than one billion users.

Brian Wieser, an analyst who covers Yahoo for Pivotal Research Group, had assumed Verizon would seek a $1 billion price cut as a result of the breaches -- if the deal went through at all.

"The worst case scenario is they outright canceled it," Wieser told CNNTech. "It's better for Verizon and Yahoo to put the standalone [Yahoo] business out of its misery and roll it into Verizon as soon as possible."

Yahoo warned investors in November there was "no assurance" Verizon would actually go through with the deal. Last month, Yahoo told investors it expected the closing date to be delayed.

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