Facebook may be on the verge of offering e-mail to the 500 million members of its social-networking site, making it the largest e-mail service on the planet.

More significantly, the offering could lead to a fundamental transformation of e-mail. Yahoo, Google and Microsoft are already scrambling to retool their e-mail services to build them more around people’s social connections. Facebook would have a tremendous advantage because it owns a vast trove of data about people’s relationships and would find it easier to graft e-mail onto its existing social services such as photo-sharing.

Facebook has invited the media to what appears to be a significant announcement in San Francisco on Monday morning, adding a prominent hint that the news could involve a new e-mail service — a press invitation bears a message icon. However, while tech blogs hummed Friday with speculation that Facebook will release “a Gmail killer,” the Palo Alto-based company declined to confirm or deny those rumors, and a source with knowledge of the social network’s plans said at least part of the speculation was incorrect — adding even more uncertainty.

If it is announced, a Facebook e-mail service would allow its more than 500 million members to communicate with anyone inside or outside the walls of the social network. If they use it, Facebook would leapfrog the 361 million global users of Windows Live Hotmail, Yahoo Mail’s 273 million users and Gmail’s 193 million users, according to comScore.

However, a Facebook e-mail service would be most remarkable not for the size of its network, but for how it could use its web of social connections to transform one of the oldest — and perhaps still the most important — functions of the Internet.

“There is a huge opportunity for these guys to fundamentally change the nature of e-mail,” said Matt Cain, an analyst for the research firm Gartner who expects Facebook to unveil an external e-mail service Monday.

Imagine, Cain said, a Facebook system that could prioritize mail from any external source based on the closeness of your relationship to the sender, or that allows you to easily flip a one-to-one e-mail exchange into a conversation with a group of friends.

Facebook now offers an internal message service that is less functional than most Web-based e-mail, and only allows members to communicate with other Facebook accounts. But Facebook may hope to use a new external e-mail service to capture even more adherents, said Augie Ray, senior analyst for social computing for Forrester Research. Forrester says that while about 90 percent of U.S. adults check e-mail regularly, only 59 percent use social networking tools such as Facebook or Twitter.

An e-mail service “makes sense just largely from a reach perspective. Facebook has grown so large that we forget that it still has room for growth,” Ray said.

And by adding e-mail to the Internet’s most popular photo-sharing service, smartphone location-sharing service and social gaming site, Facebook would make an even stronger claim as a hub of personal communications, placing “Facebook as much into competition with AT&T as it is now with Google,” Ray said.

The tech blog TechCrunch first reported in February that Facebook was working on an e-mail service, internally dubbed “Project Titan.” And while it is possible that Monday’s announcement will be something more modest, both TechCrunch and VentureBeat claimed Friday to have confirmed the e-mail service with anonymous sources.

Google and Yahoo are working to make e-mail more reflective of people’s personal connections by adding social-networking features to existing e-mail services. Google had disastrous results when it based its Google Buzz social-networking service on people’s Gmail contacts, running into a privacy Waterloo when it automatically imported people into the service. Yahoo, the most popular U.S. e-mail provider, recently launched a new version of Mail that allows users to broadcast their status on both Twitter and Facebook — just as if they were actually on those sites.

Unhappy with Facebook’s unwillingness to let people export their contacts from Facebook into a service like Gmail, Google last week blocked Facebook from allowing users to import their Google contacts directly into the social network.

Gmail is the hot property in e-mail right now, with its global audience up 21 percent during the 12 months ending in September, while Yahoo Mail and Hotmail have both lost share, according to comScore data.

Given Gmail’s momentum, a Facebook e-mail service “puts tremendous pressure on Google,” Cain said. “Gmail is the place to be, and all of sudden, in one fell swoop, Facebook can enable e-mail for 500 million users, and I would suspect there is a huge overlap.”