Good day!

I have completed my Master's Degree in Canadian University three years ago, and turned back to my home country.
Now I can apply for an Open Work Permit under the Post-Graduate Work Permit Program.
One of the requirements of the Post-Graduate Work Permit Program is
to have a valid Study Permit, which of course I do not have now. Am I still eligible to apply or not? What would you recommend?

If you do not meet all of the pre-requisites of a post graduation work permit, it would not be expected than an application for such would be approved. If this is the case, the only alternative will be to consider youth programs that may apply to you (if any) or pursue a work permit on the basis of an offer of work.