Germany's federal security council, which includes Chancellor Angela Merkel, has issued a positive response to a preliminary request for the sale by the Bremen-based Luerssen shipyard, the Bild am Sonntag said.
The boats, worth between 10 million euros and 25 million euros each, are expected to be delivered to Saudi Arabia within two years after the contract has been signed, the paper said.
Thomas Oppermann, chief whip of the opposition Social Democratic Party, voiced criticism of the project.
"The German government apparently wants to completely arm Saudi Arabia and has learnt nothing from the public protests against supplying this country with weapons," he was quoted as saying.
In December, the newspaper reported that Riyadh planned to buy at least 30 German armoured vehicles, known as Dingo 2.