Appiah, who played a key role in the club clinching a Europa League place over the weekend, met the club president on Wednesday night.
Vojvodina owner Ratko Butorovic wanted Appiah to sign a two-year deal before he departs to Ghana for the summer holidays.
But the Ghanaian pleaded with the Vojvodina owner asked for more time to consider the new two-year deal as there could be other offers.
But Appiah assured the club that he will return to sign a deal if he does not get an offer elsewhere and was delighted with their Europa place.
“I’m sorry that we did not achieve all the goals, but in the end we did manage to secure Europe,†Appiah said.
“I feel like a traitor to simply leave the club that has given me a hand when I needed it.
“In Novi Sad, I really had great conditions, worked with wonderful people and would like to stay.”
Appiah has been linked with clubs in China, UAE and Qatar.
