The former VP joined the Apple board in 2003 and owns a little over 440,000 shares, according to filings.
CNBC has reached out to both Gore's office and Apple for comment; neither side has responded.
The unanswered question is whether Gore supports Apple and CEO Tim Cook's decision to not comply with an order to help the FBI crack a phone used by one of the San Bernardino attackers, or if his sympathies lie with the government he served for more than two decades.
"The United States government has demanded that Apple take an unprecedented step which threatens the security of our customers. We oppose this order, which has implications far beyond the legal case at hand," Cook wrote earlier this week.
Gore was famous during his vice presidency for his technical savvy, including for his claim that he helped foster the creation of the Internet.
—CNBC.com's Jacob Pramuk contributed to this report