So basically the same table is shared by many client with a foreign key that identifies which data belongs to whom
As far as I know MySQL does not have any way of showing internal resource usage by user, database, or table let alone usage by a certain key in a table. When you say "storage" do you mean on-disk storage or in-memory resource usage? The former will be much easier to get than the latter especially since it item in question is one table and its resources will likely be shared among "clients".
A few ideas you can consider in roughly increasing order of difficulty:
I would start by looking at exactly why you need to know resource usage on a per client basis. Do you actually want to know the resources per client or just know how many queries they are running? If you just want to know the storage required per client then a simple/complex SELECT query to count records and field sizes would suffice.