The Nigerian was listed among the 12 persons on Jurgen Klopp’s wish list for the summer.
He is rated as one of the top talents in Europe and valued at £30m by the CIES Football Observatory.
According to Daily Mail UK, the 19-year-old alongside Bertrand Traore, Maxwell Cornet, Ryan Fraser top the list of players being considered by the Reds.
Other players are Ajax’s Hakim Ziyech, Timo Werner, Joao Felix, Nicolas Pepe, Julian Brandt, David Neres, Maxi Gomez and Felipe Anderson.
Chukwueze made 46 appearances for Villarreal in competitions with 10 goals and four assists.