City have only managed 19 goals from 18 Premiership games this season but remain in the hunt for league honours.
With that in mind the Citizens are monitoring Rantie, who looks to be on the way out at Genclerbirligi having netted six goals in 30 appearances.
Comitis, however, is mindful the 27-year-old's salary demands are likely to be high.
"I have not spoken to him," Comitis tells KickOff.com.
"You must remember he comes with a big financial salary and that's another thing one must consider."
City lost a key attacking asset in the off-season through Lebogang Manyama, who had the ability to turn defense into attack in the blink of an eye, but more importantly could punish teams and score goals.
The coastal outfit also recently sold fellow winger Aubrey Ngoma to title rivals Mamelodi Sundowns.
Comitis admitted big-name Nigerian recruit Victor Obinna is yet to come to the party in the Mother City.
"You must remember that Victor has not played for seven months prior to joining us and to be fair to him injuries also did not help his cause,” Comitis says of the former Inter Milan forward.
"Yes, I’m not happy with the shortage of goals from him but I can’t fault him or the players for their commitment to the club."