Jose Manuel Albares is set to meet the new Foreign Secretary in Brussels on Tuesday to discuss the status of the Rock.
"Spain put on the table, several months ago, a balanced and generous agreement," Mr Albares said in an interview with Spanish TV station Telecinco.
He said he was due to fly to Brussels later on Tuesday, adding: "Spain wants this agreement to be signed tomorrow [Wednesday]."
The status of Gibraltar, an enclave at the southern tip of Spain under British rule since the 18th century, and how to police the border has been a point of contention since Britain voted to leave the EU.
At the 2016 poll 95.9% of people in Gibraltar voted to stay in the EU, by far the strongest remain vote of any area that participated in the referendum.
The enclave was excluded from the exit deal reached between Britain and the EU.
Spain, Britain and the European Union agreed on December 31, 2020, that Gibraltar would remain part of EU agreements, such as the Schengen zone, and Spain would police the port and the airport, pending a lasting solution.
The European Commission and Spain sent Britain a proposal, including keeping Gibraltar's land border to Spain open, in late 2022 and ensuring the free flow of people.