The Gunners are said to be on the verge of securing the defender who is currently on international duty at Euro 2020.
However, Arsenal did not have their best last season after failing to qualify for European football for the first time in 25 years.
And Jordan thinks White might get a better deal elsewhere.
He told talkSport: “Why would he want to go? There are other stages for him which are much more convincing than Arsenal.
“If Ben White is now part of the international squad and is revered as he is because he is a premium player, why are Arsenal in the mix?
“Arsenal is everywhere. If you compare Brighton and Arsenal then yes Arsenal are a step forward. But you’re talking about someone who’s on the England squad and people inside the game think they’re an absolute Rolls-Royce.
“What good is the move to Arsenal, because they are far from where they need to be.
Will Arsenal sign White? Comments below
“There are a lot of people who were impressed with Mikel Arteta but now think that maybe it is just theory and not practice. “
Despite Arsenal’s poor form lately, Arteta is likely to keep his job and it is believed he has received financial backing from bosses to pursue the players he needs.
And if Arsenal fail to sign the Whites, it will be a blow to the club who have been looking to hire the player for weeks.
Former gunner Emmanuel Petit has acknowledged Arsenal’s common habit of not securing the players he wants.
He told the Sun: “I no longer recognize this club, I no longer see Arsenal blood on the pitch.
“It’s not about the money because Arsenal have the power to put £ 70million on a player if they want to.
“It’s all about profile, who do you want for your team in terms of character and quality? What is Arsenal doing in the transfer market?
“I don’t understand it. They spend money – a lot of money sometimes – but on the wrong player. “
And he added that if that continues to be how Arsenal handle transfer windows, their form could drop further.
“To be honest, I’m not really convinced – for four, five, six years now – with 60% of the squad,” he said.
“It’s a turning point for Arsenal, they are at the end of the world. They have to go in the right direction or they will fall and fall and fall again and it will be more difficult for them to attract players.
“You have to be more efficient in the transfer market because Arsenal cannot count on the academy players. “