The Dutch coach is currently contracted to Feyenoord but has previously announced his intentions to leave the club at the end of the season.
In an extensive managerial career, Koeman has already managed seven clubs to date, including the likes of Valencia, Benfica, PSV and Ajax.
And, according to Swans director Van Zweden, the 50-year-old's agent has enquired about him taking the reins at the Liberty Stadium.
"Albers indeed approached with the question of whether Koeman was a suitable candidate for Swansea," Van Zweden is quoted as saying by Voetbal International.
"I passed on the number of the agent to Huw Jenkins and whether there has been any contact I really do not know. I know that the club is very pleased with Garry Monk."
Therein, of course, lies the dilemma for Swansea.
Koeman is a man of considerable success, having won league and cup titles around Europe. As a player, meanwhile, the Dutchman was world-renowned, having taken part in multiple World Cups and European championships.
During his managerial career, though, the 50-year-old has not always been a success, faring significantly better at some clubs than others. He has also never managed in England before.
Remind you of anyone? Why, Michael Laudrup, of course.
And despite the success Laudrup enjoyed in his debut campaign in Wales, his tenure unravelled rather quickly in his second season at the club.
Monk knows the club inside out, has proved a steady pair of hands so far, and moving him on could just do more harm than good.
Should Swansea hire Koeman as manager next season?