From the Washington Post, on 11 November 2001:
Pakistani fears of an Indian attack on its nuclear sites were so great in the summer of 1999, after Pakistani-supported guerrillas invaded Indian territory, that military officers here secretly contacted Taliban officials about the possibility of moving some nuclear assets westward to neighboring Afghanistan for safekeeping, according to a recently retired Pakistani general officer familiar with the talks.
”The option was actively discussed with the Taliban after some indications emerged that India may open hostilities at the eastern border,” the retired official said. ‘‘The Taliban accepted the requests with open arms.”
The former official said the talks were ”exploratory” and said that no nuclear-related assets were placed in Afghanistan. At the time, Pakistan’s military and intelligence services had close relations with the Taliban, providing training, weapons and other support.
The story appears not to have been corroborated by other outlets, and it doesn’t have a named byline. I can’t find anything on this episode in the authoritative books on Kargil. But an interesting counterfactual: what if the nuclear weapons had been present in Afghanistan in September 2001?