According to AS, Mikel Arteta's side want to move quickly to secure the versatile defender, who would represent a useful addition to the right side of Arsenal's defence.
Arsenal won the Premier League this season and came agonisingly close to adding the Champions League, only to be beaten by Paris Saint-Germain on penalties in the final.
Despite that success, Arteta is keen to add further depth and competition across his squad, with uncertainty over Ben White's long-term future at the club adding urgency to the pursuit of Mingueza.
Newcastle United have also been credited with interest in the former Barcelona defender, according to the same report, with Eddie Howe keen to add cover at centre-back as part of his own squad rebuild.
Mingueza has previously been linked with Juventus, though Arsenal and Newcastle now appear to be the two clubs pushing hardest for his signature.
The Spaniard left Barcelona for Celta Vigo on a free transfer in the summer of 2022, and has gone on to make nearly 150 appearances for the Galician club, operating across right-back, left-back and centre-back during his time at Balaidos.
His versatility has been the defining feature of his rise, with Mingueza contributing seven goals and 15 assists since arriving in Vigo, numbers that reflect both his defensive reliability and his comfort progressing the ball forward.
Mingueza's representatives at Unique Sports Group have had no contact with Celta Vigo over a contract renewal, a clear signal that the player's next move will take him elsewhere as a free agent.
That stance has handed the Premier League suitors significant leverage, with no transfer fee required to complete a deal.
Aston Villa and Fulham have also previously been linked with Mingueza, while reports earlier in the year suggested Juventus made a formal approach in the January window before the move collapsed over a compensation payment that the Italian club were unwilling to make.
For Arsenal, signing Mingueza on a free transfer would offer low-risk versatility at a time when the club's title-winning squad still has areas it wants to strengthen further.
Whether Arteta can get the deal across the line before Newcastle make their own move may come down to which club can offer Mingueza the clearest pathway into regular first-team football next season.