Hi vvt,
> x86 x64 gnu guix system 1.4.0 iso requires internet connection in order to get
> installed. Same goes for i686 iso.
> 
> Why is that so? Why is there no
> iso option for installing off line? Thanks.

The reason why is because the GNU Guix System ISO is a netinstall ISO,
it has the bare minimum needed to customise the installation options and then downloads the packages when installing.

There's no option for installing offline because Guix currently doesn't offer ISO images that do that, even though it's possible.
There's previous discussion about this issue: https://lists.gnu.org/archive/html/guix-devel/2015-12/msg00452.html

Could you try this operating system definition? I think it should work(it adds XFCE and MATE).
Make a Guix checkout, and put the attached file in the gnu/system directory of the local Guix copy.
Then you can do `guix system image -t iso9660 gnu/system/offline-install.scm` to generate the offline installation ISO.