The Buckeyes gunslinger spoke about the meetings Friday at the NFL scouting combine in Indianapolis.
Haskins, 21, is expected to be a top 10 pick in the 2019 NFL Draft. The 6-foot-3, 231-pound passer completed 70 percent of his throws for 4,831 yards, 50 touchdowns and eight interceptions during his sophomore campaign at Ohio State, his first and only season as a full-time starter.
He has long been slated to be the first quarterback taken in the draft April 25 in Nashville, but Oklahoma's Kyler Murray has shot up draft boards and could challenge Haskins as the first passer off of the board.
Haskins said it doesn't matter if he is the first quarterback drafted.
"First quarterback taken, second quarterback taken, it's all a blessing regardless of where I'm going or what the pick is per say," he said. "But I don't really care how it ranks as far as QB1 or QB2. It doesn't matter to me."
The Arizona Cardinals own the No. 1 pick in the draft, ahead of the San Francisco 49ers, New York Jets, Oakland Raiders and Tampa Bay Buccaneers. The Giants have the No. 6 overall pick and are one of the first teams expected to draft a quarterback.
Despite meeting with Haskins, the Saints would most likely need to trade up to take him in the draft, as they don't have a pick in the first round. The Jaguars have the No. 7 overall pick and are expected to draft a quarterback and/or sign a veteran in free agency.
Duke quarterback Daniel Jones and West Virginia gunslinger Will Grier also said they met with the Jaguars. Missouri's Drew Lock said he met with two teams, but would not identify them. Grier said he has five more team meetings Friday.
"I always keep a mindset that I'm overlooked," Lock said. "I said it earlier, but I'm a quarterback the middle of Missouri, I'm not a quarterback from California, I'm not a quarterback from Texas, I'm not a quarterback from Florida. I went to the University of Missouri.
"I feel like I've always had a chip on my shoulder and that's going to drive me for the rest of my career. Even if I do get picked as the first quarterback, the chip is still going to be there. If I get picked in the last round, the chip is still going to be there."