The 23-year-old had a promising debut Premier League season with the Seagulls last term, missing just two matches over the entire campaign.
It was recently claimed that Brighton value White at £50 million amid interest from Spurs, United and Liverpool.
It is now reported that the Gunners have joined the pursuit of the versatile defender.
The Gunners have parted ways with Sokratis, Shkodran Mustafi and David Luiz this year, and they still have plenty of central defensive options.
Rob Holding, Calum Chambers, Pablo Mari and Gabriel Magalhaes featured last season. They could also integrate William Saliba and Kostas Mavropanos into the squad.
A new centre-back may not be a priority for them, particularly with their defensive record being the third-best in the top-flight last season.
The club are also on the lookout for a new playmaker, and it does not make sense to spend £50m on an inexperienced centre-back at the top level.
They are unlikely to spend that amount of money on White. If they are seriously interested, they could propose a possible part-exchange deal.
The Seagulls are reportedly interested in Eddie Nketiah, valued at £20m. He could be offered as a makeweight to land White’s signature.
Stats from Transfermarkt.com
Source: English Premier League – Sportslens.com