Grigg scored 28 times in 43 appearances for Wigan Athletic during the 2015-16 campaign and was included in his nation's squad for Euro 2016.
The chant "Will Grigg's on fire" has become an internet sensation and it has become well known among all 24 participating nations at the European Championships in France.
Grigg did not play a single minute of football during Northern Ireland's route to the round of 16, but a section of Hamburg supporters are keen for their club to sign the 24-year-old.
"After several proposals on social media, we have started a petition to suggest that Hamburg sign Northern Ireland international Will Grigg," read the petition.
"According to relevant trading reviews, Will Grigg has a market value of €1.5m (£1.2m). The unerring striker could fill a gap in the team, but much more than that he enjoys an international reputation and would pay the fee back through merchandising."
The Grigg chant is an adaptation of the dance classic 'Freed from Desire'.