The Welsh outfit have also made enquiries about Manchester City forward Wilfried Bony and Stoke City's Joe Allen, according to The Telegraph.
Sigurdsson is expected to be part of Swansea's squad for their Premier League opener against Southampton this weekend while his mooted £50m switch to Everton is being negotiated, although recent reports suggest that talks have stalled.
Meanwhile, Chadli is believed to have fallen out with West Brom head coach Tony Pulis, having been left out of the Baggies' pre-season tour of Austria, and is keen to find a new club.
Swansea are reportedly hoping to bankroll their bids for Allen and Bony, both of whom are former Swans players, with the cash from Sigurdsson's sale.
Elsewhere, Paul Clement's side are allegedly monitoring Arsenal's Jack Wilshere, with a view to tabling a summer bid for the midfielder.