I know that an i386 Debian can be easily installed using debootstrap on a already installed x86_64 Debian.

But the scenario is an i386 Debian is already installed on a machine that has a x86_64 CPU, and I want to bootstrap a x86_64 Debian on it. Can this be done?

The answer is yes, with a bit more extra work.

First install a x86_64 kernel, so that debootstrap can run x86_64 apps in the chroot. An i386 system can run under a x86_64 kernel, and Debian has prepared everything for you, just:

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# aptitude install linux-image-2.6-amd64
# update-grub # just in case dpkg won't run this for you
# reboot

Select x86_64 kernel in the grub menu and boot, and the rest is just a normal debootstrap process:

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# fdisk /dev/sdX # partition
# mkdir /mnt/target
# mount /mnt/target # mount all target partitions, including /boot, /home...
# debootstrap --verbose --arch amd64 unstable /mnt/target
# mount -o bind /proc /mnt/target/proc
# mount -o bind /dev /mnt/target/dev
# chroot /mnt/target
# dpkg-reconfigure debconf # set to low
# dpkg-reconfigure -a # reconfigure all packages
# aptitude # install needed packages, remember to install locales
# vi /etc/fstab
# aptitude install linux-image-2.6-amd64 # install kernel inside the chroot
# passwd # change root password
# useradd -m -s /bin/bash normal_user # add a normal user

Exit chroot and add the new entry in grub’s config file, reboot. Now you have a newly installed x86_64 Debian.

For more detail, see this chapter of Debian GNU/Linux Installation Guide and debootstrap manual.