Will the Falcons sign Sanu? Should they? Let's take a closer look.
Why it makes sense
The Falcons are starving for a second option in the passing game. Roddy White isn't a lock to be with the team and is getting older, Justin Hardy is young and may never be a true #2, and there's no one else on the roster who fits the bill currently. Sanu has been a reasonably productive option in the Bengals' offense over the last four seasons, putting up 152 receptions for 1,793 yards, 11 touchowns, and 26 grabs over 20 yards in that span. He would quite obviously give Atlanta a solid veteran receiver, and the Falcons genuinely need that.
Also, Sanu has thrown a few passes over the years, going five for five with two touchdowns meaning he can ignite an instant quarterback controversy with Matt Ryan. The Bengals have occasionally used him to great effect on running plays, so he's genuinely versatile.
Why it doesn't make sense
You've got to aim higher than this. Sanu is essentially a healthier, steadier, and slower version of Leonard Hankerson, as they're virtually the same size and have both produced fairly underwhelming careers to this point. Sanu was the Bengals' fifth-leading receiver behind A.J. Green, Marvin Jones, Tyler Eifert and Giovani Bernard in 2015, did not come down with a single touchdown, and is not exactly a big play receiver.
Sanu would be a perfectly legitimate third receiver if the Falcons upgraded at tight end and had a true #2 receiver already, but even though he's relatively young at 26, I can't see Sanu taking the kind of major leap forward that would justify the nice little contract he's likely to get.
I'm truly lukewarm on this possibility, and I suspect the team's interest in Sanu will hinge on price and whether their pursuit of other options/chances of landing a receiver they like in April dwindle. It's a quality draft class at receiver, and while the free agent market in general promise to be underwhelming, Sanu isn't the kind of potentially significant upgrade Atlanta really needs at receiver.
If the team does part ways with Devin Hester and Roddy White, you could see Sanu coming aboard even if the team does plan to draft a receiver. Call it a coin flip, but I'd prefer the Falcons spent their money elsewhere.