Messages sent to phones and posted on social media also said the government's enemies were welcome to attend the game on Thursday at the Hamdania Stadium.
Rebels in the besieged east of the city were offered safe passage.
Government forces have been bombarding eastern Aleppo for weeks and recently rolled back a rebel offensive.
The rebels have in turn been shelling the government-held west of the city.
Some 275,000 people live under siege in the east, with dwindling supplies of food and medicine.
"Oh fighters in Aleppo's eastern neighbourhoods," read one of the invitations sent out by SMS, "Aleppo Governorate invites you to attend and participate in a friendly football match, as a goodwill initiative in the context of national reconciliation."
Anyone wishing to play or attend should come "via pre-arranged routes", the message adds.
While the rebels' response was not immediately known, they have previously rejected government offers of safe passage out of the city.
The Hamdania area of the city has itself seen fierce fighting.
The Syrian government has dropped leaflets inviting rebels in the war-torn city of Aleppo to a "friendly" football match, as a goodwill gesture.