They claim the sale would be illegal under international law and accuse the oil-rich kingdom of carrying out war crimes in its military campaign in Yemen, which has killed thousands of civilians.
Spain's King Felipe VI will on Saturday begin a three-day official visit to the Middle Eastern country at the invitation of Saudi Arabia's King Salman.
Spanish media has linked this visit to a much anticipated deal to sell Avante 2200 corvettes for an estimated two billion euros ($2.1 billion).
"We can only confirm that negotiations are very advanced to build five warships which would be sold to the Saudi navy," a spokesman for state-owned Spanish ship builder Navantia told AFP.
Spain is currently the seventh largest arms exporter in the world.
Its arms exports jumped by 55 percent in 2011-15 over the previous five years, according to the Brussels-based Group for Research and Information on Peace and Security.
And its sales to Saudi Arabia, the country with the highest military expenditure per capita, are on the rise.
Friend of Saudi royals
Felipe's father, Juan Carlos, who reigned from 1975 to 2014, "had and still has an exceptional personal relationship with the Saudi royal family, which has boosted economic ties", said Ana Romero, who was written several books about the former king.
Juan Carlos was a close friend of Saudi Arabia's late King Fahd, who reigned from 1982 to 2005, and is close to his brother King Salman.
Fahd offered Juan Carlos a yacht and the two would meet frequently, in private, in France and at the Saudi monarch's luxurious palace in the upmarket beach resort of Marbella on Spain's southern coast.
Juan Carlos was credited with playing a decisive role in 2011 in helping a Spanish consortium win a contract worth 6.7 billion euros ($7 billion) to build a high-speed railway linking the holy cities of Mecca and Medina.
"There has always been a suspicion that Juan Carlos was a great lobbyist not only for Spain but also to aid his friends, close businessmen and maybe even himself," said Romero.
"Everything is different with Felipe VI: nobody thinks he can do something like that, Spanish entrepreneurs do not travel with him and his trips are much more controlled by the state."
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If the deal for the five corvettes goes ahead, it would provide jobs for over 2,000 people for several years, said Jose Antonio Fernandez Vidal, a representative of Spain's biggest union, Comisiones Obreras, in the northwestern region of Galicia, which is home to a major shipyard.
"We are awaiting this like rain in summer to create jobs in shipyards," he said.
Spain's jobless rate of 18.9 percent is the second highest in the European Union after Greece.
The contract is not a done deal yet as Saudi Arabia is slashing spending with falling oil prices having led to a drop in revenues.
And Spain faces stiff competition.
France hopes to sell another type of navy ship to the Saudis, said a source at French defence contractor DCNS.
During 2014-15 Spain was the fourth biggest exporter of weapons to Saudi Arabia after the United States, Britain and France, according to the Stockholm International Peace Research Institute.
"The question is: is the contract legal or illegal. And it is clearly illegal," said Alberto Estevez, an expert on arms sales at the Spanish branch of Amnesty International.
A 2013 United Nations global arms trade treaty bans the sales of arms which could be used in attacks against civilians or other violations of humanitarian law, he said.
A Saudi-led coalition began air strikes over Yemen in March 2015 after Huthi rebels and their allies, troops loyal to ex-president Ali Abdullah Saleh, overran much of Yemen.
Riyadh feared the Huthis would take over all of Yemen and move it into the orbit of Shiite Iran, Sunni Saudi Arabia's regional rival.
A coalition of rights groups in Spain, including Amnesty and Oxfam, has outlined dozens of alleged war crimes carried out by the Saudi-led coalition, such as the bombing of hospitals and schools.
The Spanish corvettes could be used for more than just patrols, warned Jordi Calvo, a researcher at Barcelona's Study Centre for Peace J.M. Delas.
They can be equipped with missile systems or cannons, and helicopter launch pads, he said.