Igesund led a struggling Moroka Swallows to safety when relegation was looming large, and then took them all the way to a second-placed finish before he was appointed Bafana Bafana coach in 2012.
Marques took over from Igesund and won the MTN8, but since then has struggled and the Birds only just escaped the drop this past season.
Igesund is available after SAFA decided not to renew his contract, but Swallows boss Leon Prins says they are sticking with Marques.
“First of all we have a coach and we are happy with him,” Prins tells KickOff.com. “Gordon is a great coach and we had a great relationship while he was at Swallows; we were great colleagues.
“But people like to put two and two together; now that he is available people think about Swallows. I have no plans or discussions. I don’t know what he might do in future and I wish him the best of luck.”
Swallows kick off their season with two away matches to Orlando Pirates and League champions Mamelodi Sundowns.