It was widely expected the former Bournemouth manager would be Neil Lennon’s permanent replacement at Parkhead.
However, the club put out a statement on Friday confirming “Eddie will not be joining the club, for reasons outwith both his and Celtic s control”.
Following his departure from the Cherries after relegation from the Premier League in the 2019/20 campaign, Howe sought to take a full year away from management.
A boyhood fan of Everton, he could be tempted to return to the game if Ancelotti leaves for Spain.
The Toffees who only managed a tenth place finish in the Premier League last season.
Other names on the bookmakers shortlist include Rafa Benitez, Frank Lampard and Nuno Espirito Santo.
Ange Postecoglou is still expected to become the new Celtic manager following the break down with Howe.