The 26-year-old full back, who was with Newcastle United as a youngster before joining Wigan in 2014 and Rangers a year later, has scored 25 goals and notched nearly 40 assists in his 137 games for the Light Blues.
And now the Swans could make a move for Tavernier in the summer in a bid to bolster their squad ahead of the 2018/19 campaign.
The Bradford-born right back signed a new long-term deal with Rangers earlier this season, tying him to the Ibrox club until May 2019 but, having made a handful of appearances for the Magpies in the Premier League, may fancy another crack at the English top flight.
Burnley have also been credited with an interest in West Brom’s versatile defender Craig Dawson, who can operate in central defence or at full back, while of Everton’s three options at right back - Seamus Coleman, Cuco Martina and youngster Jonjoe Kenny - Martina could be at risk this summer, amid claims the Toffees could look to reshape their squad, with even Wayne Rooney linked with a Goodison exit.
At the Liberty Stadium, the Swans also have three players at right back - Kyle Naughton, who has played 33 league games this season, veteran Angel Rangel - one start and two sub appearances - and youngster Connor Roberts, who has made just one Premier League appearance for Carlos Carvalhal’s side.
Tavernier was linked with Sunderland and Reading at the end of last year, but sought to play down the speculation by insisting he had unfinished business with Rangers.