Moss left Celtic for Huddersfield Town in June, but is already out of work.
Moss was sworn in as Huddersfield's Head of Football Operations shortly after their promotion to the Premier League, replacing Stuart Webber who had moved to Norwich City.
The Yorkshireman had previously spent seven years at Celtic, and was involved in bringing Victor Wanyama and Virgil van Dijk - now both established England top flight stars - to Glasgow.
The Sun reported in June that Moss was 'lured to quit [Celtic] by the chance to spend [Huddersfield's] millions', and the 48-year-old was, according to the Independent, the first to mention Steve Mounié, Town's £11.5 million record signing, to manager David Wagner.
But despite Huddersfield's early success in the Premier League - having recruited 13 players since Moss's appointment - the club have confirmed in a statement on their official website that they 'will now begin the search for a new Head of Football Operations'.
Celtic hired Lee Congerton, a long-term ally to manager Brendan Rodgers, as Head of Recruitment three months prior to Moss's exit.