The 19-year-old versatile forward was previously linked with a move to the Gunners last season before eventually moving to the Bundesliga side in the summer from Rennes for an undisclosed fee.
Since arriving in Germany, Dembele has caught the eye of Europe with some impressive performances, including nine goals and 19 assists in 43 games in all competitions this season.
The French youngster was also one of the bright sparks in Dortmund's disappointing 6-3 aggregate Champions League quarter-final loss to Monaco.
With Arsenal's underwhelming season continuing following their 2-0 defeat to Tottenham, with the possibility of no Champions League football next season, summer targets will likely already be looked at.
And Hargreaves believes the north London side need a right winger with Dembele being the player to fill that role in place of Theo Walcott and Alex Oxlade-Chamberlain.
"Arsenal need a right winger," he said on BT Sport Premier League Tonight. "Dembele at Dortmund, 19-year-old kid."
"He's one of the best players in the Bundesliga. He has superstar potential. He's what Arsenal need. I'm amazed that they haven't tried to get him."
With Dembele signing for Dortmund just last summer, it would certainly be quite the task for Arsene Wenger to land the Frenchman whose contract at the Westfalenstadion lasts until 2021.
However, even if Dembele was available, he will not come cheap with Manchester United manager Jose Mourinho also interested in the teenager with reports that he will offer £50m ($62.8m) for his signature.