Carvalhal departed Hillsborough by mutual consent on Christmas Eve, and is said to have made a late request to watch Swansea's 5-0 hammering from the Anfield directors' box.
Wales Online reported on Tuesday that the Portuguese boss - who it is claimed has long had admirers at the Liberty Stadium - is being seriously considered as Paul Clement's successor, and the Sun's report would appear to substantiate that early speculation.
Carvalhal, who managed Braga, Sporting Lisbon and Besiktas before being appointed by Sheffield Wednesday, led the Owls to sixth- and fourth-placed finishes in his two full seasons at Hillsborough.
However, the 52-year-old found thing tougher going this season and left the Yorkshire side - who beat Nottingham Forest 3-0 in his absence - 15th in the Championship.
Would the former Wednesday boss be a good appointment for Swansea?