Manchester City are also claimed to be keen.
Andros Townsend celebrates after scoring the first goal for Newcastle
It is claimed the Reds are tempted by Townsend's £10.5 million release clause in his Newcastle contract.
Manchester City are also credited with interest in the winger who joined Newcastle in January from Tottenham Hotspur.
England's Andros Townsend in action with Australia's Matt McKay
Newcastle's relegation was little to do with Townsend, who played well down the stretch and scored a couple of vital goals to give them a fighting chance.
This form saw him recalled to England's preliminary squad for Euro 2016, only for him to miss the final cut when the numbers were reduced from 26 to 23.
Newcastle United's Andros Townsend looks dejected
Townsend is just 24-years-old and would offer Liverpool a more direct threat out wide, while potentially asking questions over Jordon Ibe's future at the club.
His release clause is fair value and his Premier League distance cannot be discounted over a foreign import who may take time to adjust, and Townsend certainly has a point to prove after his late England omission, and the way he was cast aside by Spurs.
Newcastle United with manager Rafael Benitez shakes hands with Andros Townsend after the game