The Welsh left-back has been one of the Swans’ star turns since breaking into the club’s first XI in 2012, and is thought to be attracting serious attention from Tottenham.
But now Liverpool are also in the race, with Brendan Rodgers keen to re-invest the £60m+ the club will be getting from Luis Suarez’s move to Barcelona to strengthen his squad.
The left-hand side of his backline is a pressing concern for the Northern Irishman, which makes Davies an attractive option.
The Reds relied on right-footer Jon Flanagan in the role for their title run-in last term, with the inconsistent Jose Enrique out injured and loanee Aly Cissokho having proven to unreliable.
Spurs believe to have a trump card in the shape of Gylfi Sigurdsson – who is a wanted man at the Liberty Stadium – but Liverpool can offer the 21-year-old defender Champions League football.
Davies has been tipped to succeed at the highest level by Swansea team-mate Ashley Williams, and could be tempted by a big move after establishing himself as a capable Premier League full-back in recent times.
The Merseysiders may try to tie up a double deal involving Wilfried Bony.