Aarons has been a target since last summer when Ole Gunnar Solskjaer and the recruitment department drew up a list of Championship players who could be signed after the Premier League's transfer deadline.
United remain interested in the 20-year-old but Norwich's asking price is a stumbling block. Norwich are also keen to keep their best players in January as they attempt to win promotion back to the Premier League at the first attempt.
They are top of the Championship, four points clear of the play-off places. Aarons, who made 36 appearances in the Premier League last season, is predominantly a right-back but can also play on the left.
Sources have told ESPN that the club have received a number of loan offers for Williams but are yet to settle on a plan for his future.
Meanwhile, sources have told ESPN that United are still working on bringing in Ecuadorian midfielder Moises Caicedo but that a deal is not yet done. The 19-year-old, who has already made his senior international debut, is likely to cost around £5 million from Independiente del Valle.
Winger Amad Diallo is expected to arrive in January after a £37.2m deal was agreed with Atalanta in the summer with United confident the 18-year-old will get a UK work permit after receiving an Italian passport in December.
United have also triggered their option to extend Jesse Lingard's contract for a further 12 months.