Patrick Stump recently re-designed his official website and updated it with a viral video featuring him playing various music instruments ranging from drums, guitar and keyboard. At the end of the footage, he wrote, "I'm working on an album. I'll be writing/producing/performing everything myself. Stay tuned."
Prior to that, the site featured a quote from French author Anais Nin "and the time came when the risk it took to stay closed in a bud became more painful than the risk it took to bloom." But, it has been taken down for unknown reason.
However, when the frontman of the Fall Out Boy asked by MTV whether or not it's a solo project, he said, "I never liked that phrase, but I'm sure it will get used. 'Solo' just sounds to me like it implies that it's some kind of vacation or something, you know?"
So, it's maybe a side project similar to what Nick Jonas has done outside the Jonas Brothers. The difference is Nick forms another band The Administration, while Patrick chooses to do it alone.