Former strongman Saleh ruled Yemen for 33 years before being forced out in February 2012 and replaced by his deputy, Abdrabuh Mansur Hadi, under a UN- and Gulf-sponsored deal.
"The Supreme Security Committee received a complaint on yesterday about a tunnel and excavation works near the residence of former president Ali Abdullah Saleh," Saba reported, quoting a committee official.
"Security services immediately began legal measures and collecting evidence" from the site, on orders from President Hadi, it said.
A committee was formed to "identify the motives and parties" behind the tunnel, Saba said.
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The powerful General People's Congress party, which is still headed by Saleh, said: "We were surprised to discover an organised terrorist act targeting the nation's security, stability and unity."
The tunnel was designed to "carry out a terrorist act" targeting Saleh's "life, family, his security guards and leadership" of the party, the GPC said on its website.
The party likened the alleged plot to a June 3, 2011 explosion in his presidential compound that wounded Saleh and killed 11 people.