The boys were kicking a dog that was tied up outside a shop in the Helsingborg city centre when the elderly woman intervened. The gang then turned on her.
She was punched in the face and fell to the ground. The boys then kicked her until she started bleeding.
The woman managed to make her way home where she was bedridden for days.
The assault happened on a Monday but was only reported to the police four days later by the woman's grandchild.
Now, a man has offered the 25,000 kronor reward to help police catch the culprits, the local Helsingborgs Dagblad newspaper reports.
Torsten Persson of the Helsingborg police has spoken to the anonymous donor.
"I have told him that if he wants to do this, that is perfectly fine. It will surely lead to some unreliable tips but we'll make assessments," Persson said.
Before the reward was announced, the police had not received any tips from the public.
According to Persson it is very unusual for members of the public to offer cash rewards.
"I have experienced it a few times, but usually it is relatives who are prepared to pay," he said.
For any information to the police the public is advised to call 114 14.