The Gunners are thought to be keen on the 25-year-old striker, who has scored nine goals for the Bundesliga club so far this season.
Borussia Dortmund, Wolfsburg and Lazio have also been linked with the Hungary international, who is contracted at Mainz until June 2015.
Mainz said earlier this month that Arsenal have not been in touch over a potential deal and Szalai, thought to have a €15million (£12.5m) price tag, is not expecting to move away from the German side this month.
He told German television on Monday: "There hasn't been any connection made with the clubs who have been reported in the press, so I don't have to think about being an Arsenal striker.
"It's improbable that I'll go anywhere in the winter transfer window and that 15million euros will be paid for me."