The Gabon international has registered an impressive return of 61 goals in 97 games for Arsenal since his arrival - including 17 strikes in the 2019-20 Premier League season.
However, Aubameyang is yet to pick up a piece of silverware at the Emirates, and Wright believes that the forward should not be criticised if he does seek pastures new.
Speaking to Sporf, Wright said: "If I'm going to sit here and speak about Aubameyang at the stage of his career that he's at, maybe wanting to win things, maybe one last chance and people are saying that Real Madrid are sniffing around him.
"He's somebody with the way he's scored goals in his career, he probably wants something to show for it... I know he's won stuff in Germany.
"But if he did [leave]... if he was somebody that was tempted away, I'm not sure that people could really fault him at this stage because you look at Arsenal and the current plight, you have to say we're going through a transitional period.
"It depends totally on whether Aubameyang has the patience to wait for this to kick in but if he didn't I'm not sure at his age what people could say, he's somebody that deserves to be playing at a level where he's able to win things.
"Depending on his ambition, his people around him and what they're saying to him, how much he loves the club – and I know he loves the club immensely – you have to pray that's going to be enough for him to stay.
"But I'm not going sit here and say anything other than I wish him all the best with what he does but I pray to God he stays at Arsenal."