The 17-year-old midfielder joined the Gunners from Aston Villa in 2013 and signed his first professional contract at the Emirates Stadium the following year.
Although yet to make a competitive senior appearance for the club, he travelled on the pre-season tour of Asia this summer and featured against a Singapore Select XI.
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An England youth international previously compared to Jack Wilshere in North London, the teenager has been talked up by Roy Hodgson as a future international star. On the domestic front, Arsenal team-mates Mikel Arteta and Hector Bellerin have sung his praises in 2015.
Interest from the Posh comes on the back of a stunning FA Youth Cup Fourth Round performance at London Road last season, when Crowley inspired the Gunners to a 6-1 victory in Cambridgeshire - scoring two and assisting the other four.
Dave Robertson was in charge of the Peterborough United U18s that night, and is now first team manager after replacing Darren Ferguson at the helm back in February. That's led to whispers over pursuing Crowley, and the Posh boss did not refute the claim following a friendly defeat at Grimsby on Tuesday night.
'An excellent player'
“Everyone knows Dan Crowley is an excellent player. He played against my Posh youth team for Aston Villa when we beat them 4-0, but he then single-handedly ripped us apart the following year for Arsenal," he told the Peterborough Evening Telegraph.
“Dan is an excellent player, but he’s an Arsenal player so we will have to wait to see what develops.”
Arsene Wenger is not afraid to send Arsenal youngsters away from the club, with fellow 17-year-old Ainsley Maitland-Niles recently joining Ipswich Town on a season-long loan deal.
Crowley could join Collison
Wilshere is also an example of a player benefiting from first team opportunities elsewhere at a young age, joining Bolton back in 2010 and making a positive impact during his time at the Reebok Stadium
Whether Wenger is willing to send the diminutive Crowley down to the third tier of English football remains to be seen, but with Jack Collison now plying his trade at Peterborough there could be an opportunity for the Arsenal man to form an exciting partnership at the heart of the promotion contenders.