"Things are progressing well so therefore we'd like to be optimistic," Mr. Dastis told Reuters.
There have been fears that if a deal was not reached over the Rock of Gibraltar, a tiny piece of British territory on Spain's southern coast, it could disrupt plans for the 21-month transition period after Britain leaves the European Union on March 29, 2019.
Although 96 percent of its population voted to stay within the EU, Gibraltar will be subject to Brexit, meaning that the frontier with Spain will be plagued with the same difficulties as are posed on the border between the Republic of Ireland and Northern Ireland.
Gibraltarians Keen on Free Movement Across Border
The local government in Gibraltar is keen to preserve free movement of people across its border with Spain as many workers and tourists cross the frontier every day.
Mr. Dastis said talks between London and Madrid had started in January and there had been four meetings so far.
Both sides hope to get a deal on the Gibraltar frontier agreed by October.
"Our aspiration is that the bilateral agreement can be signed off the same time as the general agreement," he said.
In the past Spain has claimed Gibraltar as its own territory and during the reign of the dictator, Francisco Franco, the frontier remained closed.