There are also doubts over the availability of the Manchester United defender Denis Irwin and the Manchester City winger Mark Kennedy.
Staunton suffered a knee injury in Liverpool's victory over Derby at the weekend, while Holland, who won his first cap as a substitute in last month's 1-1 draw with Macedonia in Skopje, limped out of Ewood Park with a calf injury after Ipswich's draw at Blackburn.
Irwin has stayed behind at Old Trafford for treatment on a knee injury but is still hopeful that he will be able to link up with the rest of the Irish squad in Dublin in midweek. The full-back suffered the injury in a training session and missed out on United's 2-0 home victory over Leicester on Saturday.
The Republic manager, Mick McCarthy, will have talks today with his Manchester City counterpart, Joe Royle, as to the availability of Kennedy, although he seems almost certain to be ruled out by a hamstring injury. McCarthy will decide later today on possible replacements, with Sunderland's Paul Butler and Middlesbrough's Keith O'Neill among the possible call-ups.
Liverpool yesterday rebutted claims by the Bradford City chairman, Geoffrey Richmond, that he was not looked after as he would have liked when visiting Anfield for his team's Premiership fixture.
Speaking several days after his team's 3-1 defeat at Liverpool last Monday, Richmond told a national radio audience that he was disappointed with the Reds' hospitality. But Liverpool expressed surprise over the allegations and criticised the way he sought to air the matter.
The statement read: "The club was very surprised to read the comments made by Mr Richmond, because both he and his colleagues on the Bradford City Football Club board of directors were entertained in the usual welcoming manner at Anfield on Monday evening.
"Although Mr Richmond himself did not arrive at the ground until after 8pm (kick-off time), his son and other directors spent time talking with, among others, the Liverpool chairman, David Moores, and chief executive, Rick Parry, in the boardroom both before and after the game.
"We can only express our disappointment that, contrary to the Premier League Chairmen's Charter, Mr Richmond should choose to make such accusations through the media and that rather than raising any concerns he may have had at the time he should wait a week before doing so."