Hill signed an offer sheet with the Bears on Tuesday, NFL Media Insider Ian Rapoport reported, via a source informed of the deal.
New Orleans has five days to match the offer. Since Hill was tendered at the right-of-first-refusal level, the Saints won't receive any compensation if they decline.
He ended up a major disappointment in fantasy football circles, hauling in just 16 catches for 120 yards while taking a backseat to veteran tight end Ben Watson.
"Josh Hill is a guy that's been in our building a while now," general manager Mickey Loomis said last month. "He's kind of been in the background behind Jimmy Graham when he was here and Ben last year as well. He's got a lot of talent. I know this, he's a versatile tight end in that he can help us in the pass game and the run game."