The reigning NFL Defensive Player of the Year winner suffered a torn pectoral in the fourth quarter of a wild 23-20 overtime opening victory over the Cincinnati Bengals.
According to NFL Network' Ian Rapoport, Watt tore a muscle but not the tendon, which could mean his absence is as short as six weeks. There had been concerns Watt's season could be over already.
The prospect of Watt avoiding surgery will be welcome in Pittsburgh, where Steelers head coach Mike Tomlin also pointed to positive news regarding the pass rusher.
Tomlin has yet to add Watt to the injured reserve list and said: "We're not in hurry to gather information too quickly. We will see how his body responds, we'll get second and third opinions and then at the end of the week or at some point we will do what's appropriate."
He added: "I can definitively say that T.J. won't play this week, but I won't make any commitments beyond that."
The clash with the Patriots takes place on Sunday, by which time the picture regarding Watt's likely return should be clear.
Watt shared an image on social media on Tuesday of Arnold Schwarzenegger's famous "I'll be back" catchphrase, from the Terminator movie. That has been interpreted as the 27-year-old suggesting his season is not over.
Tomlin further explained Pittsburgh's stance, adding: "Let me say this, we're probably in a lot better place than we were after the game and usually that's the case.
"That's why I don't always say too much after the game, even though there might be speculation out there."