The Seagulls are understood to want to start next season with four centre-backs and are determined to sign O'Connell, after having several bids rejected by Reading for Liam Moore. Shane Duffy's groin operation has also raised doubts as to whether he will be fit for the start of the season, adding to the need for a new centre back.
The Argus reports that Brighton are readying a bid of around £6m for the defender as Chris Hughton looks for more options in defence.
The 24-year-old would be an ideal signing for Brighton after having featured regularly for the Blades across the last two season, helping them achieve promotion.
However, Brighton still face a struggle to secure the signing of O'Connell as the former Brentford captain is understood to have signed as an addition to the squad, rather than as a replacement for existing players.
Brighton finished 15th last season, seven points clear of the relegation zone, and will be hoping to build on their success this season. The Seagulls conceded 54 goals during the 2017/18 season, the lowest of any team outside of the top ten.