It would mark the latest high-profile defection by a senior North Korean envoy since the deputy ambassador in London abandoned his post in 2016.
"Acting ambassador Jo Song Gil's term was ending in late November last year and he escaped the diplomatic compound in early November" with his wife, lawmaker Kim Min-ki told reporters.
Jo, 48, has been acting ambassador in Rome since October 2017 after Italy expelled the then ambassador Mun Jong Nam in protest at a North Korean nuclear test a month earlier in violation of UN resolutions.
Italy is an important diplomatic mission for Pyongyang, as it handles relations with the Rome-headquartered UN Food and Agriculture Organization and North Korea suffers from chronic food shortages.
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Another member of the South Korean parliament, Lee Eun-jae, told reporters that the National Intelligence Service (NIS) had confirmed the envoy had sought asylum, but did not appear to know his whereabouts.
A source close to the Italian foreign ministry told AFP on Thursday the country had "no knowledge" of any asylum request from Jo.
The source said the ministry had simply received a request for the "replacement" of the diplomat, but did not know Jo's whereabouts, adding that the replacement had arrived in Rome.
The NIS briefing to lawmakers came after South Korea's JoongAng Ilbo daily reported that Jo had sought asylum in an unidentified Western country with his family.
"He sought asylum early last month," the JoongAng quoted a diplomatic source in Seoul as saying.
Italian authorities were "agonising" over what to do, the official was cited as saying, but added that they were "protecting him in a safe place".
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Jo is "known to be a son or son-in-law of one of the highest-level officials in the North's regime", the JoongAng cited an unnamed North Korea expert as saying.
Most North Korean diplomats serving overseas are normally required to leave several family members — typically children — behind in Pyongyang to prevent their defection while working abroad.
Jo, however, came to Rome in May 2015 with his wife and children, suggesting he may be from a privileged family, the JoongAng said, adding the reason for his defection bid was still unclear.
Relations between the nuclear-armed North and South Korea improved markedly last year after the tensions of 2017, with the two countries' leaders meeting three times.
Jo's defection, if confirmed, would not impact inter-Korean ties, said Koh Yu-hwan, professor of North Korean studies at Dongguk University in Seoul, "unless Pyongyang thinks the escape was arranged by South Korean authorities".
The former deputy ambassador to London who defected in 2016, Thae Yong Ho, said at the time that he had switched sides partly to give his three children a better future after being ordered to return to the North.
Pyongyang denounced him in vitriolic terms, calling him "human scum", but did not demand his repatriation.
The Kim dynasty has ruled the impoverished North for three generations with little tolerance for dissent, and the regime stands accused of widespread human rights abuses.
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