The Gunners are yet to come to an agreement over a transfer fee, and Chelsea, Everton and Manchester City are all said to be interested in the Englishman, who is contracted to the Seagulls until June 2024.
However, according to Italian journalist Fabrizio Romano, the North Londoners are confident of coming to an agreement with Brighton over a deal for the centre-back.
Romano claims that personal terms with the England international have already been agreed, and Arsenal could potentially announce a deal next week.
The centre-back has made 39 appearances for Brighton during the 2020-21 campaign.
White is believed to be valued in excess of £45m.