The news was reported in the San Francisco Chronicle on Sunday, based on a letter from the mayor sent Friday.
An email from TheStreet to both the office of Mayor London Breed and PG&E were not immediately responded to on Sunday.
City officials have been considering such a purchase, reported The Chronicle, since the power company filed for bankruptcy protection at the start of the year, following devastating fires in California that opened the company up to steep liabilities.
The paper called the offer letter the city's "most significant step to date."
If the city buys the infrastructure, the deal would form the state's "third-largest government-owned electric utility," reported the paper.
"We all agree on the importance of continuing to serve the citizens of San Francisco with safe, clean, affordable and reliable energy. PG&E has been a part of San Francisco since the company's founding more than a century ago, and while we don't believe municipalization is in the best interests of our customers and stakeholders, we are committed to working with the city and will remain open to communication on this issue," PG&E spokesman Andy Castagnola told the paper in a statement.