Adelaide United goalkeeper Eugene Galekovic has taken over as club captain, replacing sometime Qantas Socceroos defender Jon McKain.
McKain was selected by previous coach Rini Coolen after the Australian returned to the Hyundai A-League after a stint overseas, but his confidence has suffered as Adelaide's season has gone from bad to worse.
New boss Kosmina mentioned previously that he might consider taking the armband off McKain in an attempt to help him regain the form that saw him break into the national team.
"I'll have a chat with Jon and see how he feels with things," Kosmina said after taking the reins at Hindmarsh.
"He's admitted himself he's not playing well. If it's a burden (the captaincy) we'll discuss it.
Twice voted A-League goalkeeper of the year, Galekovic has remained a rock at the back during Adelaide's struggles and the widely respected 30-year-old is no doubt represents a safe pair of hands for Kosmina as he attempts to get the Reds' season back on track.