"That's the goal for me and that's what the doctors are estimating," Darnold said Tuesday during his weekly spot on ESPN New York's The Michael Kay Show.
That timetable would mean he'd have to miss only one more game, this Sunday against the New England Patriots. The Jets (0-2) have their bye in Week 4.
Speaking publicly for the first time since he got ill, Darnold sounded in good spirits, saying doctors allowed him to return to the Jets' facility on Tuesday. He can attend meetings with his teammates and coaches, but he's not allowed yet to participate in physical activity.
"I'm back doing normal things," he said. "It's just not being able to work out or get my blood pressure up in any way."
Darnold, 22, confirmed that his spleen is enlarged, a common symptom of mono. Another is weight loss, but he has dropped only two pounds because he started eating extra meals and snacks as soon as he learned of the diagnosis. That, he believes, will allow him to stay in relatively good football shape during his layoff.
He also revealed that he was under the weather for the Jets' season-opening loss to the Buffalo Bills, estimating he was 80 to 85 percent for the game. The former USC star said he had trouble sleeping and was dealing with cold sweats in the days leading up to the game.
"After the game, my body decided to shut down," said Darnold, who passed for only 175 yards in a lackluster performance. "When I came in that Monday morning, I was feeling terrible. Tuesday morning was when it really hit. That's when we did all the tests."
Late Wednesday night, Darnold received a knock at his apartment door from coach Adam Gase, who broke the bad news. The quarterback thought it was a "sick joke" at first, but he noticed Gase, offensive coordinator Dowell Loggains and the trainer weren't laughing.
Darnold watched Monday night's loss to the Cleveland Browns with his parents at his New Jersey apartment, admitting he got emotional when Trevor Siemian suffered a season-ending ankle injury in the second quarter.
"When it initially happened, I actually had a little episode," he said. "I went in the [next] room and started screaming into a pillow and was punching my pillow as hard as I could. It was tough. You never want to see that for a teammate."
Siemian suffered significant ligament damage and will require surgery, so the Jets -- reeling on offense -- will turn to former third-stringer Luke Falk against the Patriots. It will be Falk's first NFL start.
It looks bleak for the Jets, a 22.5-point underdog, but Darnold insisted the season isn't lost.
"If I get back for Philly and we go on a little run -- obviously, we've got our work cut out for us -- but anything is possible," he said.
Darnold said he doesn't know how he contracted the viral infection. He managed to laugh, saying he noticed a woman at the stadium holding a sign that proclaimed she was the person who gave him mono.
"For the record," he said, "I never met that girl in my life."