I want to create a class which stores DataTables, this will prevent my application to import a list of details each time I want to retrieve it. Therefore this should be done
Static variables aren't thread safe per-se. You should design with thread safety in mind.
There's a good link to get you started: http://en.csharp-online.net/Singleton_design_pattern%3A_Thread-safe_Singleton
Apart from this, I would strongly recommend you to use a more modern approach than the legacy DataTable. Check out the Entity Framework or NHibernate. Implementing them in your datalayer will allow you to hide database details from the rest of the software and let it work on a higher level abstraction (POCO objects).