Speaking after regular talks in Brussels, neither side would forecast exactly when a free trade agreement - discussed for over 15 years - could be reached.
But Sheikh Abdullah bin Zayed al Nayhan, speaking for the GCC presidency, said: "There is a political willingness... Both the EU and the GCC have demonstrated a readiness to accelerate this process.
"That might take a few months, maybe a bit longer. We don't know."
He added that the currently €40 billion worth of trade could be more that doubled by a successful deal.
Benita Ferrero-Waldner, the EU external relations commissioner, said she hoped that an agreement could be reached "hopefully by the end of this year", adding that "substantial progress has been made".
"We do hope to come to agreement as soon as possible."
Ursula Plassnik, the Austrian foreign minister whose country currently holds the EU's presidency, said: "We are quite confident, given the atmosphere of the meeting today, that we will move on quite rapidly."
The GCC groups Bahrain, Kuwait, Oman, Qatar, Saudi Arabia and the United Arab Emirates.
The EU expanded from 15 to 25 nations in May 2004, taking in 10 mostly former communist countries in central and Eastern Europe.