Flaherty underwent imaging tests on his right shoulder Tuesday. He has not thrown off a mound since spring training opened.
"It would be nice to know what's going on with him and what the plan will be with him moving forward," manager Oliver Marmol said Thursday. "Our hope is we get it here pretty soon."
Flaherty, 26, was 11-8 with a 2.75 ERA in 2019, went 4-3 with a 4.91 during the pandemic-shortened 2020 season and 9-2 with a 3.22 in 17 starts last year, when he was slowed by an oblique injury.
Reliever Giovanny Gallegos was expected to start workouts Friday after a late arrival.