The EU expects Turkey to extend the accord to include the partitioned Mediterranean island before it begins entry talks on 3 October.
Extension of the customs union to include Cyprus is sensitive in Turkey because it is seen by some officials as tantamount to a de facto recognition of the internationally accepted Greek Cypriot government.
Negotiating the text
"We have had negotiations on the text of the protocol. There is a text on which we agreed," the official told reporters on Friday.
Turkey and the European Commission, the EU's executive, will start an exchange of letters on the text, the official said.
"We asked the European Commission to send the letter on the text of the protocol. If the letter is the same text we agreed, then it will be approved," he said.
Parliament must approve the protocol for it to take effect.
Turkey, which won a date to start long-delayed entry talks at a EU summit in December, recognises only a breakaway Turkish Cypriot enclave in the north of the island since invading in 1974 in response to a short-lived Greek Cypriot coup.
It keeps about 30,000 troops in the isolated, poorer north. Ankara has said it wants UN efforts to reunite the divided island revived before its EU talks date in October.