To ensure a smooth transition, we’re providing a three-month sunset period so you have sufficient time to find an alternative feed-reading solution. If you want to retain your Reader data, including subscriptions, you can do so through Google Takeout.
(Emphasis added by me.)
Source.
And for a how-to, see below.
Login to your Google Reader account and click on the gear on the right-hand side of your web browser. Select Reader Settings from the drop-down menu.

Click on the Import/Export tab in the Google Settings page. Here you will find a link to Download your data through Takeout.

Click on the link to Download your data through Takeout and you will be brought to Google's Takeout service. Login again to your Google account, if needed.

Make sure the Choose Services button at the top of Takeout is selected and Google Reader is noted in the box on the center of the screen. Click on the Create Archive button at the bottom to create a backup of your Google Reader account.
You will then jump to the download screen where you will see the progress of your backup. My backup was small so it was already completed by the time the page opened. The files for your Google Reader account will be bundled into a zip file and can be downloaded to your computer.
Click on the download button to start transferring the Google Reader files to your computer.

Locate the downloaded zip file on your Mac using Finder and double-click on it to extract the files to their own folder. The Reader folder will contain a handful of .json files and a subscriptions.xml file. You can ignore (but not delete) the .json files.
Open your new RSS client and use it to import the subscriptions.xml file that you just downloaded and extracted.
Source.