The 23-year-old has impressed with the Seagulls during the 2020-21 campaign, with 39 appearances in all competitions.
Arsenal continue to be strongly linked with the England international, but the Gunners are struggling to come up with the fee required to begin talks with the centre-back.
According to The Sun, Everton are prepared to pay £50m for the Englishman.
The report adds that the defender is aware that there appears to be a battle for his signature ahead of the new season.
White has three years left to run on his contract at the Amex.