LONDON—British transport company National Express is in talks to acquire rival operator Stagecoach Group in an all-share deal, offering scope for cost savings and underpinning their recovery from COVID-19. The tie-up, which would value Stagecoach at about 445 million pounds ($609 million), comes as government support to help the companies get through the pandemic is due to expire. National Express has bus and coach operations in Spain and Britain, runs school buses in the United States, and has a German rail contract. Stagecoach, solely focused on Britain, is the country’s biggest bus and coach operator. The company was founded by Brian Souter and his sister Ann Gloag in Perth in 1980, starting out with just two buses bought with their father’s redundancy money. They still own stakes in the company—Souter has about 14.55 percent and Gloag around 10.47 percent, based on Refinitiv data. Under the terms of the potential takeover, …