Qatari Minister of State for Foreign Affairs Ahmad Abdullah al-Mahmood said after talks with EU officials in Brussels that after 18 years, the two sides were now "very close" to concluding the agreement.
"According to what the experts told us, at the end of June I think they will find a solution and it will be signed by the end of the year. I hope so."
Abdullah al-Attiyah, secretary general of the GCC, added: "we would like to see this negotiation on the FTA concluded soon.
EU External Relations Commissioner Benita Ferrero-Waldner said the two sides had made very good progress and were now "closer than ever to a conclusion.
"We have to work closer together to reach a conclusion," she said," adding that it was her conviction that the two sides needed to be more ambitious in their relations.
She said a number of "very technical questions" remained to be settled, including in the area of export duties.
The GCC is a loose economic and political alliance that comprises Kuwait, Qatar, Oman, Saudi Arabia, Bahrain and the United Arab Emirates.
Earlier this year al-Attiyah expressed frustration at the length of time it had taken to negotiate the agreement, blaming "endless" conditions by the European bloc.
He complained that while EU companies won very big contracts in the Gulf Cooperation Council countries, they could not export their products to European markets.
Talks between the group and the EU began in 1990 but were slowed by the GCC agreeing only in 1999 to move towards forming a customs union and a new EU negotiating strategy adopted in 2001 to include the services sector in the talks.
The European Commission said in January 2006 it expected to complete the trade agreement "in the near future".
As well as seeking to boost trade and investment, the agreement would also cover political issues such as human rights, illegal immigration and the fight against terrorism.
