The Telegraph suggests that the Swans are set to go after the Manchester United legend as they contemplate replacing Francesco Guidolin in the not too distant future.
It is understood that the Italian is a 'dead man walking' following a poor start to the new Premier League season, doubled with his treatment of a couple of players in particular - Ki Sung-yueng and Neil Taylor.
The South Wales outfit were keen on Welsh great Giggs in the summer but chairman Huw Jenkins saw any potential move blocked by the club's new American owners.
However, the report indicates that Guidolin could now be sacked before the October international break which has prompted the speculation surrounding Giggs.
The 42-year-old left Old Trafford in the summer following the arrival of Jose Mourinho and has been linked with a number of jobs in recent times.