Bollocks. If you were offered 300k a week to remain in London playing for a top club your Sri Lankan ass would sign faster than you can say "Wenger out", regardless of who the manager was.
Alexis simply has more leverage in negotiations simply because:
A) His position and how few top strikers there are in the world
B) The fact he's more prepared to move abroad as he's played in several countries already and is used to it.
Alexis' people have just seen what the likes of Bale, Ronaldo, Pogba etc etc have signed for and he wants some kind of parity with them and thus they're driving a hard bargain in negotiations like Theo's people were a few years ago.
As you've seen with slimeballs like Pogba, Mkhirtyian etc, a lack of CL football or the downward spiral of a club has nothing to do with it, if the money is there. It has nothing to do with managers and if anything, Wenger's a more enticing figure for players to sign simply because of his reputation in the game (fairly or unfairly).