Costa is without a club after agreeing to terminate his contract at Atletico Mineiro after six months at the Brazilian size, and the Gunners have been linked with a stunning move for their old foe.
Arsenal manager Mikel Arteta is seeking to bolster his front line in the January transfer window, with Pierre-Emerick Aubameyang in exile at the club and currently at the Africa Cup of Nations, while Folarin Balogun has joined Middlesbrough on loan.
Alexandre Lacazette and Eddie Nketiah are both also out of contract in the summer, and they have combined to score just three league goals between them this season.
Signing 33-year-old Costa would be a short-term option, but with the striker now available for free it could be a win-win deal for club and player.
The Brazil-born Spain international has been linked with several clubs in his adopted home nations, with LaLiga sides Caldiz and Elche, plus LaLiga2 outfit Eibar said to be interested.
But now Arsenal have joined the race, according to Goal, with claims the Gunners have held talks with the striker and his team.
The report suggests Arsenal transfer chiefs have been in 'informal consultation' with the ex-Premier League hot shot and there has been no official offer put on the table, yet.
Costa is currently on holiday in Spain as he assesses his options for his next career move, with Sau Paulo giants Corinthians also said to be keen to keep him in Brazil, but he is said to be in 'no hurry' to make a decision.
Costa joined Atletico Mineiro in August 2021 and enjoyed a successful, albeit short, spell at the club with five goals and one assist in 19 appearances as they won a domestic league and cup double.
He even made headlines in December for driving around in a tractor after the club's trophy success.
Now the eccentric frontman could be offered a path back to English football, but this time with his old London rivals Arsenal.
Costa loved scoring against the Gunners during his Chelsea career, with a stunning record of six goals and five wins in six appearances against the north Londoners.
The frontman left the Blues with an overall record of 58 Premier League goals in 120 appearances over three seasons at Stamford Bridge, where he lifted the Premier League and League Cup double in 2015, adding another league crown in 2017 before his exit to Atletico Madrid.
He continued to haunt the Gunners with the Spanish club, too, as he scored the goal that kicked Arsene Wenger's team out of the Europa League semi-finals in 2018 during the legendary Frenchman's final season in charge.