Thanks for your reply Adeyemi.
Seems getting reminded about a specific message in private channel (same way like getting reminded in public channel) is not possible.
For public channel messages Workflow template called Follow up on a message works fine (using More actions menu), but this mechanism is not available for private channels.
Also Remind tab for private channels messages works completely different, compared to messages in public channels and it does not suit intended need.
Thank you very much for your support.
Damir