Boss Unai Emery has been impressed with the 20-year-old’s displays at the U20 World Cup this summer.
Zagadou helped France keep two clean sheets in the group stage before they were eliminated by the USA in the Round of 16.
The highly-rated centre-back earned a place in Paris St-Germain’s academy at the tender age of 12.
But in 2017, Borussia Dortmund announced his signing on a free transfer, handing Zagadou a five-year deal.
According to The Mirror, Arsenal have now placed the player on their shortlist of wanted youngsters.
But the report adds they are aware that they may not have adequate finances to complete a deal.
Zagadou, who stands 6ft 5in tall, would add aerial prowess to an Arsenal defence which currently lacks height.
The youngster has excelled at every level of France’s youth set-up from Under-16s.
The Gunners are already trying to sign Saint-Etienne teenager William Saliba.
But the Arsenal hierarchy are reluctant to match the £25m Saint-Etienne want for the 18-year-old.
They are particularly hesitant over agreeing to loan Saliba back to his current club.
Emery is believed to be keen to see the club’s limited £45m budget spent on players who can make an immediate impact on the first team.
Shkodran Mustafi, Rob Holding, Sokratis and Laurent Koscielny are the Spaniard’s current options in central defence.
But Koscielny is considering quitting Arsenal after being offered two-year contract to return to France with Lyon.
The veteran, looks set to leave the Emirates this summer after talks over a new deal broke down.
It would mean the club captain leaving departing just 12 months short of a decade-long stay at the Emirates.