Antitrust officials at the Justice Department and the Federal Trade Commission confirmed that they are separately working towards new guidelines for vertical mergers but caution that creating a joint protocol won’t be easy.

Vertical merger guidelines, which outline how antitrust enforcers assess the impact of deals between companies that compete in different markets, haven’t been updated since 1984. “It was quite relevant back then but it must not be right now,” since deal-making has changed over the past 35 years,...