Arteta told reporters in his pre-match press conference that he knows Stones well from his time as assistant manager at Manchester City but is not considering a January move:
"No truth at all. John is a player that I really like and we followed him before we signed him when I was at City. I worked with him for many years and I know him well, and obviously when I look at centre-backs he has got many attributes that I like from one. But we are not interested in him."
Arsenal do have issues in defence with Calum Chambers (ACL) and Kieran Tierney (shoulder) long-term injury victims, while Sead Kolasinac will miss Saturday's visit from Sheffield United, per PA Sport's Mark Mann-Bryans:
The Gunners have also struggled at the back in 2019-20, conceding 31 goals in 22 Premier League games, and look in need of reinforcements in the January window.
Arteta has prioritised signing a "box-to-box midfielder and a defender" in the January transfer window, according to Sam Dean at the Daily Telegraph.
He added that he is hoping to strengthen his squad but will not rush into any signings: "Yes, but it has to be the right player, in the right context that financially we can compete and we can attract and all these factors, if you put them together, are not easy in this market."
Stones has only made nine Premier League starts for Manchester City in 2019-20 because of injury and a lack of form, but manager Pep Guardiola does not appear to have lost faith in the 25-year-old:
The centre-back made his first Premier League start in over a month on Sunday in Manchester City's 6-1 win over Aston Villa and will be hoping to keep his place for Saturday's visit from Crystal Palace.