The Gabon international is yet to commit his future to the north London club with less than a year remaining on his current deal.
Aubameyang once again proved his worth to the Gunners last season, scoring 29 goals in all competitions, including a brace in the FA Cup victory over Chelsea.
The 31-year-old carried his good form over to the new campaign, scoring the winning penalty in the Community Shield to beat Premier League champions Liverpool at Wembley.
The Gunners have already completed the signings of Willian and Gabriel Magalhaes from Lille, while Atletico’s Thomas Partey is a priority signing.
Wright believes persuading Aubameyang to extend his stay at the Emirates is Mikel Arteta’s most important task this summer.
‘To be honest, I think he will be the most significant signing Mikel can make,’ Wright told Good Morning Britain.
‘We do need to make that happen, simply because of what he brings to that team. When you look at the chances created for Arsenal, they were 16th in the league and he still scored the amount of goals he scored.
‘So if you can imagine, we can start creating more with the players we have signed – the Willians and people like that – then he is going to score more goals.
‘It is imperative that he signs.’
‘I keep saying the same thing,’ the Spaniard told BT Sport. ‘I try to do my job, which is convince him that he is in the right place, that he has the environment here to produce the moments like he’s done today and he’s done here three weeks ago.
‘I am very positive that he’s going to sign but a lot of time there’s a lot of things involved in a contract deal and we are trying to show him.’