The 19-year-old, who has scored two league goals for Villa this season, is believed to have attracted the attention of Manchester United and Arsenal after breaking into the first team at Villa Park.
However, Steve Bruce's side have tied Davis to a new deal which will run until the summer of 2020.
"It's a great feeling to have signed a new contract. This is another milestone for me this season – I had my first start and my full league debut then an international call-up and this is another one," Davis told the club's official website.
"The hard work continues, now. I've got to keep working and reach that next milestone."
Davis joined Villa from non-league club Biggleswade Town in 2015.