A deal could be announced within days, said the person, who did not want to be identified because negotiations are still ongoing.
Any deal that is reached could form the basis for federal legislation and would likely shape efforts by the Federal Communications Commission to broker an agreement on the contentious issue, which has pitted the nation's big phone and cable companies against many big Internet companies.
The FCC has been holding talks with a handful of large phone, cable and Internet companies - including Verizon and Google - to try to reach some sort of industrywide compromise on net neutrality that all sides can accept. FCC Chairman Julius Genachowski is seeking to adopt rules that would require phone and cable companies to give equal treatment to all broadband traffic traveling over their networks.
Public interest groups and a number of big Internet companies, including Google and online calling service Skype, say such rules are needed to prevent broadband providers from becoming online gatekeepers. They are particularly concerned that the phone and cable companies could start charging extra for priority access, or could slow or even block Internet phone calls, online video and other Web services that compete with their core businesses.
But the phone and cable companies argue that after investing billions in their networks, they need to be able earn a return on their massive investments by offering premium services. They also insist that they need flexibility to manage network traffic so that high-bandwidth applications don't eat up too much capacity and slow down their systems for everyone else.
While there is consensus that broadband providers should not be allowed to block or degrade Internet traffic, the FCC talks have yet to produce an agreement. Two big sticking points center on whether broadband providers should be allowed to offer premium services and whether net neutrality rules should apply to wireless networks, which tend to have more bandwidth constraints than landline systems.
In a statement Wednesday, Verizon said it has been in talks with Google for nearly 10 months to try to strike some sort of compromise on net neutrality. It added that it remains committed to the discussions taking place at the FCC and is "optimistic this process will reach a consensus that can maintain an open Internet and the investment and innovation required to sustain it."
Google had no comment.
Google and Verizon are already business partners since Google's Android operating system powers Verizon Wireless's Droid smartphone. The Droid is the biggest competitor to Apple Inc.'s iPhone, which is available only through AT&T Wireless in the U.S.
An FCC statement said only that "the broad stakeholder discussions continue to actively include Google and Verizon."
AT&T Inc., which is also taking part in the FCC talks, said it is "not a party to the purported agreement between Google and Verizon" and remains "committed to trying to reach a consensus on this issue through the FCC process."
Several public interest groups, meanwhile, voiced concerns that a deal between Verizon and Google would allow broadband providers to offer premium services and would not apply to wireless networks. Josh Silver, founder and president of the group Free Press, warned that an agreement would amount to "a bold grab for market power by two monopolistic players" and would "effectively create two Internets where application and content innovators have to ask Verizon and Google for permission to reach mobile Internet customers."
"The point of a network neutrality rule is to prevent big companies from dividing the Internet between them," said Gigi Sohn, president and co-founder of the group Public Knowledge. "We do not need rules to protect Google and Verizon, but we need a rule to protect the customers of Google and Verizon and the competitors of Google and Verizon."
The talks at the FCC are also focused on establishing the agency's authority to regulate broadband. The agency has been scrambling to develop a new regulatory framework since a federal appeals court in April cast doubt on its jurisdiction over broadband - including its ability to mandate net neutrality - under existing rules.