In the AMC drama's second season, Walt allowed Jesse's girlfriend Jane (Krysten Ritter) to die, unbeknown to Jesse.
Paul told The AP: "If Jesse finds out the true story of that, I mean heads are going to roll really. So maybe that might be the end of the show? I don't know."
Paul also praised his character's evolution over the programme's run, claiming that "more [of Jesse's] layers are revealed" as Breaking Bad continues.
"He's just a mixed up kid that got lost on this path and he's constantly struggling to... find his way and to keep his head above water," he said. "[Viewers] sympathise with this character. People are rooting for him."
Breaking Bad creator Vince Gilligan previously suggested that the show could end after five seasons.
The drama's fourth season continues on Sundays at 10/9c on AMC.
> Breaking Bad: 'Thirty-Eight Snub' recap
Watch a promo for the next episode of Breaking Bad below: