KYIV, Ukraine—Ukraine’s prosecutor general’s office said Friday it is reviewing past investigations into the owner of a gas company linked to former U.S. Vice President Joe Biden’s son, raising the possibility of restarting probes amid pressure from President Trump.

For the past several months, the Trump White House has pushed the authorities in Kyiv to investigate Burisma Group, a big gas-production company, and the role there of Hunter Biden, who served on its board, along with actions of Mr. Biden when he was overseeing...