Dzsudzsak, 29, has been made available for transfer by Turkish side Bursaspor after a disappointing debut campaign in which he recorded just three goals during 23 Super Lig appearances.
But despite this underwhelming return as the Green Crocodiles limped home 11th, a number of suitors have come forward to buy the 78-times-capped winger who will perform a prominent role for his country at Euro 2016.
Serie A side Sampdoria and Hertha Berlin from the Bundesliga have made contact with his camp, while Wahda and Al Ain are leading the charge from the Arabian Gulf League.
The Clarets were the first to begin talks last week, though they risk being nudged aside by the UAE’s most-decorated club. A pursuit of a foreign wide man capable of playing on the left has seen Zlatko Dalic’s outfit make a €4 million (Dh16.5m) offer, according to Turkish sports magazine Fanatik.
This is higher than the €3m (Dh12.4m) bid from Hertha and anything which Wahda have offered at present. The ability of the top-flight runners-up to offer tax-free wages which would be superior to any bid from Europe could also swing the pursuit in their favour.
Dzsudzsak is able to play on both flanks and made his name on the left as a youngster at Dutch outfit PSV Eindhoven, prior to a transfer to then big-spending Russian outfit Anzhi Makhachkala worth a reported €20m (Dh82.7m) in June 2011.
An injury-plagued spell ended a year later with a €19m (Dh78.5m) move to Dynamo Moscow, where he scored 13 times in 112 appearances before departing to Turkey for just €1.6 m (Dh6.6m) in August 2015.
Any final decision about his future should arrive after his commitments at the Euros in France are over. Hungary are expected to struggle in Group F, where they play their first game on Tuesday against Austria.
Al Ain want a winger to compliment right-footed speedster Danilo Asprilla, with Brazilian centre midfielder Fellipe Bastos surplus to requirements in their four-player foreign quota.
The 26-year-old – who scored six times in 39 appearances since a summer switch from Vasco Da Gama – has been linked to Al Ahli Jeddah.
For Wahda, Brazilian defensive midfielder Denilson is an injury doubt for the start of the season and the 2017 AFC Champions League play-off entrants could choose to ditch him no matter how his recovery goes as they pursue an increased goal threat.
A previous attempt to recruit forward Ciel after his contract at champions Al Ahli expired was terminated after problems were highlighted during a medical.
