The Midlands outfit want to bring in a replacement for Matheus Cunha, who has left to join Manchester United for £62.5 million.
Abline appears to be a good option for Wolves, but Nantes are demanding a £43.3m fee for the 22-year-old, per Sunday Mirror (August 10, Page 71).
Ligue 1 club Paris FC submitted a £21.65m offer but that was turned down by their French counterparts.
Nantes are looking to drive an auction, with Eintracht Frankfurt also keen on the player.
Abline is a versatile forward who mainly plays as a striker but can also operate on the wings.
He previously played for Stade Rennais before joining Nantes in 2023, initially on loan that was later made permanent.
The Frenchman has scored 16 goals and provided three assists in 60 appearances in all competitions for the Canaries.
Abline has proven his skills in France and can also be a success in the Premier League.
But it remains to be seen whether Wolves will fork out a £43.3m fee for the 22-year-old.
Cunha went to Man Utd, while Rayan Ait-Nouri left to join Manchester City.
Goncalo Guedes was sold to Real Sociedad, and Nelson Semedo departed the Molineux Stadium on a free transfer.
Wolves have added Fer Lopez, Jhon Arias and David Moller Wolfe, but they still need reinforcements.
Bringing in a new right-back is a top priority, while they also need to add some depth in the midfield.