BEIJING—China is offering foreign technology firms better access to the country’s fast-growing cloud-computing market, people briefed on the matter said, as Beijing fashions a compromise in a tech sector the U.S. wants opened as part of a trade deal.

Premier Li Keqiang disclosed the proposal to allow trial operations for foreign cloud-service providers at a Monday meeting with about three dozen corporate chieftains, including those from International Business Machines Corp., Pfizer Inc., Rio Tinto PLC, BMW AG and Daimler AG....