White has been a key man in Brighton's first 10 matches this season and has made the step up from the Championship look relatively easy.
The classy 22-year-old has operated in the backline but has been comfortable when asked to play as a defensive midfielder.
Brighton were determined to keep their star man last summer and rejected three bids of more than £20m from newly-promoted Leeds United.
White had previously enjoyed a successful loan spell with Marcelo Bielsa's team in the Championship but Brighton were steadfast and held on to their academy graduate.
The January transfer is fast approaching and Brighton are bracing themselves for more enquiries, for a player who could potentially fetch around £50m.
But Albion head coach Graham Potter is non-fussed by the continued speculation and insists his star-man will not have his 'head-turned' as they prepare for Monday night's Premier league clash against Southampton.
"I have no worries about Ben getting his head turned," said Potter. "He is a level headed guy who wants to play football and of course he wants to do it at the highest level, just like you want all those players to have those ambitions.
"He gets on with his work and he was totally professional in the summer despite the noise from outside the club, which you can’t control.
"He knows that, he’s a smart guy and we will carry on with our work and help him to enjoy his football, which is the most important thing."
Brighton, who are 16th with 10 points from 10 matches, could also face a battle to keep hold of their midfielder Yves Bissouma.
The Mali international has been impressive for Brighton this season and it has not gone unnoticed by Gunners boss Mikel Arteta, who is said to be a huge admirer of the 24-year-old.
The powerful and competitive midfielder signed for Brighton from Lille in July 2018 for £15m and is contracted with Albion until 2023.
"I have never been a coach that worries about losing a player," said Potter.
"If you worry about losing players to teams higher up the hierarchy – because that’s ultimately what it is – and the club think selling the player is the right thing to do, then it’s a result of doing something well.
"I don’t think you should ever worry about that. It’s part of football and a lot of it is talk, speculation or nonsense.
"There’s always truth as well somewhere, but I am not worried about anything. I am just helping the players to improve, to get them to the highest level of performance that I can and then we will see."