The game has been under the spotlight since the sides were drawn together in February, with Ireland one of Europe's most outspoken critics of Israel's war in Gaza. There have been numerous protests in Ireland asking for the team not to fulfil the fixtures with Israel.
Ireland were due to hold the press conference on Saturday, but shortly before the scheduled start at 10:15 local time (09:15 BST), reporters were informed that this would now take place following the team's training session at the stadium in Debrecen.
That was due to commence at 11:00 local time, but two hours later the Ireland team were still inside their hotel.
Ahead of Ireland's opening Group B3 game away to Kosovo, which they lost 1-0, captain Dara O'Shea told reporters that the players would meet on Friday to discuss a plan of action for the game against Israel.
Football Association of Ireland (FAI) members voted in November for its board to request that UEFA suspend Israel from European competitions, but a motion in favour of proceeding with the fixtures was passed at an FAI EGM in July.
All of Israel's home games are scheduled to take place in Debrecen, and Ireland moved their home fixture, set for October 4th, to Serbia. That game will be played behind closed doors.
Tensions increased further when Ireland manager Heimir Hallgrimsson used the word "genocide" in a press conference last weekend. The Israeli FA responded by calling his remarks stupid and ignorant.
Israel's assault on Gaza has been described as genocide by UN experts and rights organisations, an allegation Israel strongly rejects.