/usr/bin/tlmgr is in texlive-base 2016.20170123-5.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/bin/../share/texlive/texmf-dist/scripts/texlive/tlmgr.pl
/usr/bin/../share/texlive/texmf-dist/scripts/texlive/tlmgr.pl