SSRS data source - specify machine account credentials

When I create websites in IIS that connect to a SQL Server database I can set the website to run as the machine account and give permissions to that machine account within SQL Server, which allows me to specify what the websites on that server can access within SQL Server without having to either embed a username and password within the connection string or set up security individually for each user that will access the website.

I would like to do the same thing for reports within SSRS, but I cannot find any option for doing so...

I'm using SQL Server 2008 R2, and Reporting Services is installed on a different server to the databases that the reports access.

Is this possible?