A German official on tour with Merkel said on condition of anonymity: "There is a clear political desire on both sides to get a swift resolution to the disputed points."
Germany holds the EU presidency until the end of June.
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 EU is the GCC's top trade partner, while the Gulf group ranks number six for the 27-nation union.
Other issues Merkel wants to discuss with Middle East leaders are Iran's nuclear programme and her efforts to revive the stalled peace process between the Israelis and Palestinians.
In addition to Saudi Arabia, Merkel has visited Abu Dhabi and Egypt during her four-day trip. On Tuesday, she heads for Dubai and Kuwait.