Sasman has been put on the transfer list, together with Siphosakhe Ntiya-Ntiya and Lazarous Kambole, after he joined Chiefs ahead of the 2020/21 season.
Widespread reports have suggested the 25-year-old defender is likely to join the Dube Birds, and it is believed to be part of a swap deal that saw Njabulo Ngcobo moving to Naturena.
Swallows chairman David Mogashoa has now confirmed his side's interest in snapping up the former Ajax Cape Town left-back.
"We are interested to sign him. We are still negotiating with him," Mogashoa tells snl24.com/kickoff.
Amakhosi are currently in a rebuilding phase following their CAF Champions League runners-up finish last season as well as their two-window FIFA transfer ban.
Swallows FC are set to take a decision on George Lebese, Mogakolodi Ngele and Mark Mayambela, who have been training under coach Brandon Truter's watchful eye.