Citing information made available by unidentified intelligence sources, Spiegel said the plant was in an inaccessible mountain region in the west of the war-ravaged country, two kilometres (1.2 miles) from the Lebanese border.
It is deep underground, near the town of Qusayr and has access to electricity and water supplies, the magazine said in a pre-released version of the story released ahead of Saturday's publication.
It said it had had access to "exclusive documents", satellite photographs and intercepted conversations thanks to intelligence sources.
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Western experts suspect, based on the documents, that a reactor or an enrichment plant could be the aim of the project, whose codename is "Zamzam", Spiegel said.
The Syrian regime has transferred 8,000 fuel rods to the plant that had been planned for a facility at Al-Kibar, it added.
In 2007, a bombing raid on an undeclared Syrian nuclear facility at Al-Kibar was widely understood to have been an Israeli strike, but it was never acknowledged by the Jewish state.
Spiegel said North Korean and Iranian experts are thought to be part of the "Zamzam" project.
The Lebanese militia Hezbollah, which supports al-Assad's regime in the bloody conflict in Syria, is guarding the secret project, it added.