It's understood the Gunners will sign the Brighton defender, 23, for £45million plus add-ons which would take the deal to £50m.
White enjoyed a brilliant first season in the Premier League with the Seagulls and a move would mark another step up in his budding career.
The move has been backed by Arsenal legends David Seaman and Ray Parlour but Jordan was left wondering why it could happen.
The talkSPORT host believes there are better things out there for White, who's currently with the England squad at Euro 2020.
On the prospect of White joining Arsenal, a bemused Jordan said: "Why would he want to go there?"
"With respect to Brighton it's a step up but there may be other steps available to him that are far more compelling than Arsenal.
"If Ben White is now in the international squad and revered the way he is, because he's a top quality player, why are Arsenal in the mix? Arsenal are all over the place.
"If you're comparing and contrasting Brighton to Arsenal then yes it is a step up but if you're comparing somebody who's in the England squad that people in the game think is a Rolls Royce then what is the move he's making to Arsenal for?"
Jordan also has his reservations about Gunners boss Mikel Arteta, who could only guide them to an eighth-placed finish in the Premier League.
He added: "They are a long way from where they need to be and there's a lot of people looking at Arteta, me included, who started out thinking this guy's got the chops but are maybe thinking he's all theory and not enough practice."