While not a traditional "download manager," OptinMonster can gate a download link behind an email form.
EDD is a full-featured digital eCommerce plugin. Even for free downloads, you can force users to provide an email at checkout.
Now go lock that first file and start growing your subscribers! Have you tried any of these plugins? Let me know in the comments which one worked for your site.
Download Monitor lets you create "download locks" that require form submission.
Do you want to grow your email list while giving away free eBooks, checklists, software, or PDFs?
The most effective way to do this is to —requiring users to enter their email address before they can access the file.