Both websites cited anonymous sources who are familiar with the deal and put a purchase price at 60 million dollars (£36m).
Facebook spokesman Tucker Bounds said the company does not comment on rumours and speculation. Titan Aerospace representatives did not respond to requests for comment.
If Facebook does buy Titan Aerospace, the purchase could fit with the goals of CEO Mark Zuckerberg's Internet.org project.
The Facebook-led partnership, which includes Qualcomm Inc, Samsung and Nokia, was launched last summer and aims to connect the more than five billion of the world's seven billion people who are not already online. Presumably, Internet.org could use Titan's solar-powered atmospheric satellites to serve as airborne wireless access points.
Google, which is not a part of the Internet.org effort, launched a similar undertaking earlier this year with the goal of getting everyone on Earth online. Called Project Loon, the effort launched internet-beaming antennas aloft on giant helium balloons.
Titan's drone-like atmospheric satellites, which are still in development and not yet commercially available, can stay in the air for as long as five years, according to reports. Titan's website cites a wide range of uses for the drones, including atmospheric and weather monitoring, disaster response and voice and data communications. The last two could be reasons for Facebook's interest in Titan.
But Zuckerberg said last week at the Mobile World Congress wireless show that access connectivity is not the main obstacle to getting the world online.
He said more than 80% of the world's population live in areas with 2G or 3G wireless access. More important, he said, is giving people a reason to connect: basic financial services, access to health care information and educational materials.
Facebook's acquisition of a company called Onavo last autumn also fits with Internet.org's vision. Onavo develops data compression technology, which helps applications run more efficiently. This is especially important in developing countries, where people have access to much slower internet speeds.