Costa's time at Chelsea is all but over after Blues manager Antonio Conte informed him via text message that he is not part of his plans for the coming campaign. The Spaniard is seemingly desperate to return to Atletico Madrid, but Serie A outfit AC Milan have registered their interest in the combustible forward, who is valued at £44m (€48.6m, $57.3m) by the Premier League champions.
Arsenal signed striker Alexandre Lacazette for a club-record fee earlier this summer but Wright is eager to see Arsene Wenger's men pursue a deal for Costa, who won the Premier League twice during his three seasons with Chelsea.
The former Crystal Palace hitman knows a deal to bring the 28-year-old to the Emirates Stadium is nigh-on impossible but is keen to see Arsenal "ask the question" while they still can.
"To be honest, as fanciful and unlikely as it may be, I'd also like to see Arsenal at least dipping their toe in the water for Diego Costa as well," Wright was quoted as saying by the Daily Star.
"For all the talk of him going back to Spain, nothing's been done yet, so at least ask the question. Because while he can be troublesome, he is also a brilliant, proven Premier League goalscorer."
Chelsea are keen to accelerate Costa's departure for west London but would be more than reluctant to sell him to Arsenal, who do not seem to be at all interested in a move for the former Atletico star and have a troubled situation with one of their own attackers, with doubts surrounding the future of talismanic forward Alexis Sanchez.
Conte's men have already drafted in Alvaro Morata as Costa's replacement this summer, but the former Italy manager is keen to strengthen his squad with further additions before the end of the transfer window.
Chelsea have loaned out 24 players already this summer and will no doubt farm out more before the transfer deadline, but Conte is desperate to see fresh faces arrive amid concerns over their squad depth and ability to compete both in the Premier League and the Champions League.