The Hungary international has netted 12 times in 22 Bundesliga outings this season, earning him plenty of admiring glances - with Arsenal said to be among those monitoring his progress.
The 25-year-old, who spent three years with Real Madrid's reserve side between 2007 and 2010, makes no secret of the fact that he sees his long-term future away from Mainz.
He is, however, prepared to wait for the right move to arrive, with his contract set to run until 2015.
A big-money offer from a club competing in Europe could be tabled this summer, forcing a decision to be taken, but for now both Szalai and his current employers insist no transfer has been discussed.
"Of course I want to play regularly in competitions like the Europa League and UEFA Champions League," Szalai told Sport-BILD.
"But I am not thinking about a transfer at this point in time. I am unfazed by gossip and rumours."
Mainz general manager Christian Heidel added: "We have not received any enquiries from any clubs regarding Adam Szalai."