The Dutchman is set to leave Feyenoord at the end of the season, and would reportedly be interested in taking over at the Liberty Stadium.
Koeman, 50, was mentioned as one of the favourites to succeed Michael Laudrup when the Dane was sacked last month.
Swansea have placed Garry Monk in temporary charge, but Koeman is understood to be a favourite to land the position full time.
And speculation is set to intensify after Swansea’s Dutch director John van Zweden claims Koeman’s agent Guido Albers has been in touch regarding whether his client would be a candidate for the job.
He said: “Albers has indeed approached me asking if Koeman is a suitable candidate for Swansea.”
Swansea look set for a mid table finish, with the team currently 14th in the table, four points above the drop zone.
Chairman Huw Jenkins will let Monk see out the remainder of the season, before considering the managerial position, although Koeman’s experience is likely to be a big appeal.