Cooks is the fastest wideout available, and he set records last season with 1,730 receiving yards from 128 receptions, winning the Biletnikoff Award along the way.
He also recorded more plays over 20 yards than any other player in this year's Draft class.
"We've been talking a lot on and off," Cooks told the New York Post. "I took a visit and I think the visit went great. It's one of those things. I feel like they're pushing for me, but who knows?
"It's an amazing fit. I feel like the Jets are on the rise. They're doing great things. I just feel like they need to add one more thing to their package. I feel like if they had a speed receiver they'd be complete. We'll see."