Roy, 33, has not played in any of the four games against the Black Caps because of a back problem.
None of England's initial 15-man squad for the World Cup were due to play in the three games against the Irish, the first of which is on Wednesday.
England are due to confirm their party for the World Cup in India next week.
Roy, who was part of the England team that won the World Cup on home soil in 2019, has been struggling with back spasms.
"It's a frustration and the most frustrated person is Jason," England captain Jos Buttler told Test Match Special.
"Obviously he is desperate to play and be fit. He is moving very well but is not quite fit to play a game of cricket today.
"That's a frustration but that is where we are at, at the moment."
England are due to fly to the World Cup on 27 September, which is the day after the third game against Ireland in Bristol.
They have named an entirely different 13-man squad for that series, captained for the first time by Zak Crawley.
But when asked if Roy, who has not played competitively since the final of The Hundred on 27 August, might feature against the Irish, Buttler said: "Yes, I think so.
"The Ireland squad has obviously been selected, but we still have a few days should we wish to make any changes, or expose anyone to some games of cricket. We can do that."
Roy had to watch on his home ground of The Oval on Wednesday as Ben Stokes took his record for the highest score by an England batter in an ODI.
Stokes' 182 eclipsed the 180 Roy made against Australia in Melbourne in 2018.
When England named their squad for the series against New Zealand, selector Luke Wright said the same 15 players would be the group for the World Cup.
But Buttler and coach Matthew Mott have since intimated the changes could yet be made, leaving the door open for Harry Brook to force his way in. The final squad does not have to be confirmed until 28 September.
Brook, a late call-up to the New Zealand squad, is playing at Lord's on Friday and is in the squad for the Ireland series.
Leg-spinner Adil Rashid and pace bowler Mark Wood were also once more on the sidelines for the finale of the series against the Black Caps.
Rashid has been managing a calf problem, while Wood has not played at all since the Ashes.
"Adil is progressing," said Buttler. "He is someone who is so important to us as a side.
"His skill set is very unique so he's always someone we are very much looking after. He should be good for when it matters."On Wood, Buttler added: "Obviously the World Cup is the priority for him. He's looking good, bowling well, and going all in the right direction.
"Again he is someone who offers a unique skill set so he's someone we are taking great care of."
England open the defence of their world title against New Zealand in Ahmedabad on 5 October.