Duke Tobin, Bengals director of player personnel, told reporters that the team hasn't received any "hard" offers for the No. 5 pick.
"I think people are waiting to see what's going to happen at 3 and 4," said Tobin.
It's widely assumed that Trevor Lawrence and Zach Wilson will be the first two players taken by the Jacksonville Jaguars and New York Jets.
The San Francisco 49ers already made a move up to get the No. 3 pick in a trade with the Miami Dolphins. Mac Jones has been the most-discussed player landing with the Niners, though Trey Lance and Justin Fields could still be in the mix.
Depending on what the 49ers do, teams lower in the draft that have interest in one of the remaining quarterbacks could look to move up. There's also a wealth of talent at other positions, including wide receivers Ja'Marr Chase, DeVonta Smith and Jaylen Waddle, tight end Kyle Pitts, linebacker Micah Parsons and offensive tackles Penei Sewell and Rashawn Slater to choose from.
The Bengals could go any number of directions based on their current roster. It wouldn't be a surprise to see them take a pass-catcher or an offensive tackle, but if they want to secure more picks with the idea they could get a high-quality player lower in the first round, trading back could make sense for them.
Cincinnati has eight picks in the 2021 NFL draft.