Yes, there are various ways depending on what you’re looking for.
There’s the Status/Progress feature of projects (Progress tab) that includes the toggle “Remind me to update the status every Friday”. You’d do this in 10 projects for 10 separate statuses this way.
Or, make one project for this. Make the 10 people members. Make one recurring task that’s the reminder. All project members will receive the notification. They can each have a section in the project for their regular statuses, or each have one task and their regular statuses can be subsections/subtasks.
I have a template for my clients that’s an Asana version of something I used for many years to collect leads’ last week’s goals/statuses, this week’s goals, and any blocks/issues.
There are probably other ideas too.
Hope that helps,
Larry