Huddersfield Town and Crystal Palace are also keen on the 22-year-old, according to The Mirror.
Aarons has emerged as a January transfer window target for Steve Bruce after finding his first-team chances limited at St James' Park this season.
He has made only two substitute appearances in the Premier league and has not started a game since the EFL Cup defeat to Nottingham Forest in September.
The former England Under-20 international could move next month and, with Villa boss Bruce looking for low-cost cover for his injured forwards, a deal could suit all parties.
Aarons is under contract at Newcastle until 2021, having signed a new five-year deal in August 2016.