The Swans had targeted the Belgium international last year before he joined West Brom from Tottenham.
Baggies manager Tony Pulis dismissed speculation linking Chadli with a move away after a reported argument between the two earlier this summer.
But Swansea continue to monitor the 28-year-old, particularly as their midfielder Gylfi Sigurdsson remains a prime target for Everton.
The Toffees have had a £40m offer rejected for the Icelander, who is valued at £50m.
Should the move go through, Swansea head coach Paul Clement would be eager to use those funds to strengthen his squad.
The Swans were interested in Las Palmas playmaker Jonathan Viera, though the Spanish club's asking price of around £25m was deemed too high.
Swansea City are interested in signing West Brom winger Nacer Chadli.