You need to add spotify ppa repository in order to install 64 bits version:

# nano /etc/apt/sources.list.d/spotify.list

add this ppa:

deb http://repository.spotify.com stable non-free

# apt-key adv –keyserver keyserver.ubuntu.com –recv-keys 94558F59
# apt-get update
# apt-get install spotify-client

Run spotify-client