Although there are offers from elsewhere, the left sided midfielder appears to be giving Swallows priority.
Zwane adds that he is still waiting for a new deal to be tabled.
AmaZulu are believed to have already put in an offer to lure Zwane back to his hometown and Thanda Royal Zulu FC are also said to be interested in the 33-year-old.
With Swallows having signed another left winger, Ryan Botha from Thanda, it could signal that Zwane may not be in their future plans.
“At the moment I am still waiting for Swallows to get back to me about the possibility of a new deal. I have been told that Leon Prins will get in touch with me next week.
“I will know where I stand after I have spoken to Swallows,” says Zwane, noting that he has enjoyed his second spell at the Birds.
The former Bafana Bafana midfielder adds that should the Birds choose not renew his contract then he will move to wherever he will be happy.
“I just want to be happy wherever I am because that is what matters the most to me. If Swallows choose not to extend my contract, the club that I play for next will not be determined by its location. I can play for any club anywhere for as long as I am happy there,” he says.
Capped nine times for Bafana, the winger has played at Manning Rangers, Golden Arrows as well as a stint with Rostov in Russia.