He made his comeback from a six-week lay-off against Manchester City late last month and scored in United's shock League Cup victory.
Aarons also netted against Crystal Palace in late August, bringing him to the attention of the English public.
Man City are said to be tracking his progress, ready for an offer in January.
Aarons suffered his injury in training last week and didn’t feature against West Bromwich Albion on Sunday.
According to a report from NUFC the 18-year-old will miss the fixtures against Queens Park Rangers on November 22 and West Ham United a week later.
Aarons said on Twitter: “Everything happens for a reason. I’ll be back...again.”