Our company has about 10 different SSRS reports. We would like to allow users to navigate from one report to another simply by selecting the report from a dropdown list. Is this possible?
Yes. You would need to write your own custom web app to interact with each SSRS instance.
You would do all of this using the .NET library around SSRS, it includes methods and such for interacting with reports in SSRS. A small/basic example: http://www.aspsnippets.com/Articles/Local-SSRS-Report-in-ASPNet-Tutorial-with-example.aspx