Saved as reports (Report Builder) should have option to allow only for "Owner"

Dear community,

Currently, if I create a new report from Report View, using Save As…

These report will be accessible by everyone. I think this is OK in some case, but for big organization, this can lead to a lot of junk reports I don’t want to see.

I think the Report should have option to permit only “Owner” of the report.

Are there anyway to achieve this?

Thanks!