Brighton have still not received a transfer offer that meets their demands, with him set to leave on his summer break after the end of Euro 2020 with his future still uncertain.
The 23-year-old was part of England's Euro 2020 squad, and while he did not play in the tournament, he will still be allowed to have some time off before returning to Brighton's pre-season camp.
White's long-term future is still unclear, with Arsenal registering their interest in the Brighton defender.
According to journalist Pete O'Rourke, White is leaning towards a move to Arsenal, with him eager to move to the Emirates.
While speaking on The Football Terrace, O'Rourke said "Ben White really wants this move even though there was a bit of late interest from Everton."
"The defender has his heart set on a move to the Emirates. I think he wants to stay down south predominantly as well so that puts Arsenal in a good position to finalise this move."
However, a transfer is still far away from being completed, with Arsenal yet to offer a deal that Brighton are willing to accept.
While Brighton will not publicly state an asking price for White, yet they are reportedly considering a hefty fee, especially after a standout debut season in the Premier League.
The Argus claimed that "There is currently nothing on the table they would accept."
The Brighton-based newspaper claim that Arsenal have the greatest interest in the England international, and that Brighton will only accept a substantial offer for him.
The paper states that a "well-place source" has informed them that "it would take a number which makes it 'nonsensical to say no' to move White".
This could prove to be a big issue for Arsenal, who need several players coming in this summer to help in their rebuild after a tough Premier League season.
White made 39 appearances in all competitions last season for Brighton, and he is under contract with the Seagulls until June 2024.