The 25-year-old - who is under contract with the Bundesliga club until 2015 - has scored nine goals so far this season, prompting admiring glances from a number of clubs, including Borussia Dortmund, Wolfsburg and Lazio.
Szalai is understood to have a €15million release clause written into his current deal, but according to German newspaper Bild, that can only be activated at the end of the season, ruling out a possible switch during the January transfer window.
"Arsenal haven't contacted us," claimed Mainz manager Christian Heidel. "We don't want to let our striker go in the winter transfer window. But that's another situation if someone willing to pay 20 million Euros for him."
Only yesterday it was reported that Gunners boss Arsene Wenger was seeking an alternative traditional striker to Olivier Giroud, who arrived at the Emirates Stadium during the summer from Montpellier.
When asked about reported interest from Arsenal, Szalai insisted he was in the dark, telling Kicker: "I don't know anything about it. The season is long, I don't know what will happen at the end of it.
"My aim is to collect as many points as we can and get as far as we can in the German Cup. Summer we can talk about what happened."
Szalai has also gained notoriety for his on-pitch celebrations - with the Mainz striker performing the world-renowned 'Gangnam Style' dance - a tribute to Korean pop sensation Psy, after he scores a goal.
It's up for debate how well such celebrations would go down in the Premier League with the north Londoners. But, you can watch a video of the Hungarian in action and judge for yourself below…