You want to configure SSRS to use basic authentication with a SMTP Server – FORGET IT – it is not supported…but You can try a way to get around this problem…have a look at this solution…
- You need your own virtual SMTP server and set it to relay messages with basic authentication to the remote server.
- You need to install the SMTP feature on your Windows Server instance. You can do this by Add Feature in Windows Server 2008 /2008 R2 or Add/Remove Programs in earlier version

3. We select SMTP from the list of feature and install with all required role services.


Click on “Close” after the installation completes.
4. After installation,You have to set up new SMTP server to relay emails via the remote SMTP server. Click on Start, Administrative Tools and then on Internet Information Services (IIS) 6.0 Manager

5. Expand the tree and go to virtual SMTP server.

6. Choose Properties (right click on virtual SMTP server). Under the general tab, select the IP address of for the SMTP server.

7. Use Access tab and click on “Relay”. It is recommended to restrict access to this virtual SMTP server only to computer with SSRS installed, so if You wish to limit the computers that are allowed to relay through this virtual SMTP server by specifying them explicitly then keep the “Only the list below” option selected and add the IP addresses

8. Accept configuration – “OK” and go to the Delivery tab. On the Delivery tab click on “Outbound security”.

9. THE MOST IMPORTANT ELEMENT TO CONFIGURE: Select “Basic authentication” and specify the username and password that you need to use to authenticate to the remote SMTP server and Accept configuration with “OK”

10. Go to “Outbound connections” and set the remote SMTP Server port number.


11. Finally go to Advanced and spcify your remote server address in the “Smart host” textbox.


12. The last element of your configuration is to configure SSRS – You can do that by running the Reporting Services Configuration Manager utility.

13. Connect to you SSRS instance and then click on the “Email Settings” option.
Set the email address that will be shown as the sender when SSRS sends emails.
In the “SMTP Server” textbox type the IP address that you selected for the virtual SMTP server which was configured by you in this case.

Click on “Apply” and then “Exit” after the settings have been applied successfully.
Congratulations!
You have just configured Reporting to send emails via the local virtual SMTP server which will relay the emails using the Remote SMTP server with basic authentication