According to The London Evening Standard, Costa was told in January that he could leave Chelsea this summer.
It has also been reported that the 28-year-old striker has his heart set on returning to Spain in the summer transfer window.
Atletico Madrid are claimed to be interested in signing the Spain international striker, but the La Liga outfit cannot register any new signings until January due to a transfer ban.
Arsenal legend Wright has suggested that the Gunners should make a move for the Chelsea star this summer.
“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 wrote in The Sun.
“For all the talk of him going back to Spain, nothing’s been done yet, so at least ask the question. Because for all he can be troublesome, he is also a brilliant, proven Prem goalscorer.”
Costa is one of the best striker in the Premier League, and there is no doubt that he has been a success for Chelsea since joining the Blues from Atletico in the summer of 2014 for a transfer fee reported by The Guardian to be worth £32 million.
The 28-year-old was a key figure in the Blues’ Premier League-winning campaigns of 2014-15 and 2016-17, and is a proven goalscorer at this level.