After impressing for RB Salzburg last season, the 18-year-old attacking midfielder has attracted the attention of some of Europes top clubs.
The Gunners are long time admirers of the teenager and are hopeful they can tempt the Austrian champions to sell as Unai Emery looks to build a squad capable of breaking into the top four in the coming season.
With a Champions League campaign high on RB Salzburgs agenda, its thought they would be reluctant to sell before the January transfer window. However, that timeline could change if Arsenal match their valuation, according to Football Insider.
Hes already been capped four times by Hungary and Arsenal will face fierce competition from Borussia Dortmund and Juventus among others for his signature.
Szoboszlais agent has also confirmed a number of Premier League teams are interested in his client, but declined to name any of the clubs.
"I can confirm a number of the top Premier League clubs are interested in Dominik but at this point I can not confirm or deny specific clubs," Szoboszlais agent, Matyas Esterhazy, told football.london.
"My client is focusing on his current club and the upcoming challenges of the next season both in the league and the Champions League."
The price tag would suit Arsenals £45m transfer budget. Another season without Champions League football has taken its toll financially on the north London club and this kind of signing could be an indication of their approach as they try to re-establish themselves among Europes elite.
Arsenal are yet to secure any incomings and have already missed out on Lorient youngster Alexis Claude-Maurice and Belgium international Yannick Carrasco.
With some key departures already announced this summer and some uncertainty surrounding Lucas Torreira, there are serious concerns about the look of Arsenals squad ahead of the new season.
The Gunners finished fifth in the Premier League last term and lost 4-1 to Chelsea in the final of the Europa League.