The 23-year-old front-man heads for the Hungarian top flight to play some first team football and will remain with Diósgyőri VTK until 30 June, 2014.
Futacs, a former Hungary Under-21 international, joined City as a free agent in July 2012 following a successful spell with Portsmouth.
He made 12 appearances and scored twice for the Foxes in all competitions last season, before spending a month on loan with fellow Sky Bet Championship club Blackpool.
He most recently featured for City in a 2-1 FA Cup defeat to Huddersfield Town in February.