The Yahoo deal team is pushing back hard against any attempts to negotiate the price down, the paper said.
Last month Yahoo said at least 500 million of its accounts were hacked in 2014 and in a statement Verizon said it had been made aware of the breach immediately but had limited information about the matter.
U.S. senators accused Yahoo of "unacceptable" delay in discovering the hack and urged the U.S. Securities and Exchange Commission to investigate whether Yahoo and its senior executives fulfilled obligations to inform investors and the public about the hacking attack.
Verizon and Yahoo both declined to comment.
In July, Verizon agreed to buy Yahoo Inc's core internet properties for $4.83 billion in cash, setting the stage for a big new internet push by the telecom giant.
(Disclosure: CNBC has a content-sharing partnership with Yahoo's finance site.)