The report claims that Liverpool, Chelsea and Leicester have been monitoring the Hungary international though the latter are in pole position to sign him having already held talks with his club.
The Foxes are keen to strengthen their squad this summer and their newfound reputation as a Champions League club means they have more opportunities to sign big-named stars.
Hungary's Adam Nagy in action with Austria's Zlatko Junuzovic
However, Leicester boss Claudio Ranieri has made it clear that his side will instead keep to the tried and tested method of unearthing Europe’s next top stars and Nagy fis into that category.
The 21-year-old has been a key performer for Hungary so far at the European Championships, helping the unfancied side progress to the latter stages after topping Group F containing Portugal, Austria and Iceland.
Energetic, comfortable with both feet and an eye for a pass, Nagy has been making great strides over the past 12 months and many feel the time is right to move on to a bigger club.
Iceland's Jon Dadi Bodvarsson in action with Hungary's Adam Nagy
The report goes on to mention how the player has a release clause as low as £2 million, a fee which allows Leicester to seemingly take a low-risk gamble on a potentially superb player.
Despite his young age, Nagy has already reached double figures for caps on the international stage after making his debut against Northern Ireland at Windsor Park almost 12 months ago.
Northern Ireland's Kyle Lafferty in action with Hungary's Adam Nagy