The official says Germany has set aside €135 million ($180 million) in next year's budget to pay for about a third of its cost.
Dolphin-class submarines are capable of carrying nuclear-tipped missiles, but there is no evidence that Israel has armed them with such weapons.
Israel already has three Dolphin submarines from Germany - one half-funded and two entirely funded by Berlin, a staunch Israeli ally.
The official, speaking on condition of anonymity because of the sensitivity of the issue, said Wednesday a 2005 agreement between the two nations included an option for another subsidized submarine which was now activated at Israel's request.
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