Despite the arrival of attacker Takumi Minamino from RB Salzburg earlier this month, Jurgen Klopp is still keen to strengthen his forward line, which has seen Rhian Brewster depart on loan to Swansea.
Foot Mercato claim Chukwueze has been “promised” to a Premier League club and the Reds could be the side to benefit from the arrival of the 20-year-old.
The Nigeria international, who was linked with Liverpool last summer, played down the interest at the time.
“I am aware that there are several interested teams, but I am still a Villarreal player and there is nothing concrete,” he told Marca.
Chukwueze was one of the breakout stars of LaLiga last season, with the winger scoring eight goals in 38 appearances in all competitions in his first season at the top level.