People close to the negotiations who were not authorized to speak publicly about them said an agreement could be reached as soon as next week. If completed, Google, whose Android operating system powers many Verizon wireless phones, would agree not to challenge Verizon’s ability to manage its broadband Internet network as it pleased.

Since the court decision, involving Comcast, in April, the F.C.C. has been trying to find a way to regulate broadband delivery, and that effort has been the subject of a series of private meetings at the agency’s headquarters in recent weeks. At the meetings, officials from the nation’s biggest Internet service and content providers, including Google and Verizon, have tried to reach a consensus on how broadband Internet service should be regulated in light of the decision. Those meetings continued this week, apart from the talks between Google and Verizon.

The court decision said the F.C.C. lacked the authority to require that an Internet service provider refrain from blocking or slowing down some content or applications, or giving favor to others. The F.C.C. has since sought another way in which to enforce the concept of net neutrality. But its proposals have been greeted with much objection in Congress and among Internet service providers, cable companies and some Internet content producers.

A spokesman for Verizon said that the company was still engaged in the larger talks to reach a consensus at the F.C.C. and declined to comment on other negotiations. A spokeswoman for Google also declined to comment. While a deal between Google and Verizon would affect only those two companies, it could sway the opinions of lawmakers, many of whom have questioned the wisdom of the F.C.C.’s plans to oversee broadband service.

At issue for consumers is how the companies that provide the pipeline to the Internet will ultimately direct traffic on their system, and how quickly consumers are able to gain access to certain Web content. Consumers could also see continually rising bills for Internet service, much as they have for cable television.