A centre-forward remains a priority – though no deal appears close as things stand – while Sheehan also wants a left-sided defender and a wide player.
Stamenic started his professional career in his homeland with Porirua-based Western Suburbs, then spent a year with Team Wellington before moving to Europe to join Copenhagen.
He had a spell on loan at another Danish side, HB Koge, before moving to Red Star in 2023.
Stamenic helped Oympiacos win the Greek league and cup last season, having also won domestic doubles with both Red Star and Copenhagen.
“His arrival strengthens an already robust midfield unit and will allow us to play with the relentless energy and adaptability that we want to be hallmarks of our team,” said Swansea director of football Richard Montague.