James Taylor of Nottinghamshire is to captain the side, which will have an experimental look because several contenders for a place will have been involved in the third Test against West Indies, which is scheduled to finish next Tuesday.
However, West Indies tourists who are not picked for that Barbados Test may be added to the 11-man squad for the Ireland game.
With regular one-day captain Eoin Morgan at the Indian Premier League, Taylor will skipper the side in just his 18th one-day international.
Gregory, 22, a right-arm batsman and medium-pacer, and the 23-year-old left-arm spinner Ansari are in contention to make their senior debuts.
And there are three other possible debutants in the form of Hampshire batsman James Vince, Northamptonshire’s left-arm seaming all-rounder David Willey and Kent wicket-keeper/batsman Sam Billings.
Yorkshire wicket-keeper Jonny Bairstow is understudying Jos Buttler in the West Indies at the moment but has been named in the squad.
And he could be joined by leg-spinner Adil Rashid, and seamers Mark Wood and Liam Plunkett, depending on whether any of the trio are called into the Test side.
England disappointed at the World Cup earlier this year, failing to qualify for the knock-out stages, and with places now very much up for grabs, next week’s Dublin match will be seen as a big opportunity by the members of the new-look squad.
The most experienced member of the squad is the 30-year-old Yorkshire seamer Tim Bresnan, who played the most recent of his 84 one-day internationals in March last year.
He has yet to feature for England since Peter Moores was re-installed as head coach but toured with the Lions this winter and netted with the World Cup squad in Australia in January.
Steven Finn of Middlesex has 56 one-day caps and is another seamer who will be keen to perform well, with doubts surrounding the one-day futures of James Anderson and Stuart Broad.
National selector James Whitaker said: “We are expecting a very competitive match against a talented Ireland side and this fixture gives us a great opportunity to look at players who have performed well in county cricket and for the Lions.
“We are starting to identify players we believe can make a real impact in??limited overs cricket in the next four years as we build towards the ICC Cricket??World Cup in 2019 and these players have a huge opportunity to stake a claim for??further opportunities this summer.
“We will add a number of players to the squad once the side for the final Test against West Indies has been selected.”
Taylor made his England debut against the Irish in 2011 and said: “To be??given the opportunity to lead your country is a huge honour.
“There are still some very experienced and talented cricketers in that team,??who I’d have been delighted to have as my captain, so it is a privilege and one??I’m going to relish.
“It’s going to be brilliant leading an England team in a one-day??international. We know it will be a tough game against Ireland and this match??provides a great chance for us all to show we can play a huge role in limited??overs cricket in years to come.”
England squad to play Ireland: James Taylor (captain), Alex Hales, Jason Roy, James Vince, Johnny Bairstow , Sam Billings, Zafar Ansari, Tim Bresnan, Lewis Gregory, David Willey Steven Finn