Thanks for your quick answer.
I checked the settings as you suggested and the blog is already set to public. And I still can't import the comments.
Though, I noticed that the client enabled google+ comments for the blog which automatically disable the possibily to edit the settings to public or private.
So I disabled the option "Use Google+ Comments on this blog", then I could edit the setting either to public or private. I also realized the comments didn't show on the blog page either.
Maybe the Blogger Importer didn't recognize the google+ comments which I think is used as a third party.
Do you think there is a way to pull the google+ comments into wordpress?