Justin Sullivan/Getty
Facebook CEO Mark Zuckerberg.
The report does not quote Zuckerberg directly, but said he made the comments at an event hosted in honour of "Friends Day," which marks the 12-year anniversary of Facebook's founding.
Facebook currently has 1.5 billion users, according to the company, meaning that the 3.5 billion user increase would more than double its size.
Facebook also published a study that claimed everyone on the network was connected by 3.75 degrees of separation, lower than the six degrees it's commonly accepted connects everyone.
"We want to finish connecting everyone [and] we're going to do it in partnership with governments and different companies all over the world," said Zuckerberg, according to USA Today.
The company has recently faced criticism in India over its "Free Basics" programme which aims to bring more and more people online. However, activists argue that Facebook will have too much control over the websites and services people can use. Facebook denies this.
Zuckerberg also talked about the company's $2 billion (£1.4 billion) purchase of Oculus, a company that makes virtual reality headsets and software.
"You can convey emotions through text, and photos, and videos get [you] closer, but actually being able to feel like you are there is going to be amazingly powerful when the medium becomes mature," he said, according to USA Today.
"We're reaching this period where video is going to be primary thing we use on the Internet, because of the emotional weight of it," he continued.