Dempsey was forced to withdraw from the team that thrashed Scotland 34-13 because of a hip injury and Murphy, his replacement, went on to produce a man-of-the-match display.
The star turn by Murphy, who has since been struck by an Achilles problem, confronted Ireland coach Eddie O'Sullivan with a major selection headache.
But O'Sullivan will give the rivals as much time as possible to prove their availability before making a final decision.
There are two confirmed changes to the side that dismantled the Scots with Paul O'Connell displacing Mick O'Driscoll and Rory Best coming in for Bernard Jackman.
Munster lock O'Connell was a second-half substitute against Frank Hadden's side but continued his comeback from his back injury with an impressive display against Cardiff last weekend.
Jackman pays the price for some wayward throwing in the line-out by losing his place to Ulsterman Best, a more solid performer at the set piece.
O'Sullivan said: "Girvan and Geordan are both struggling at the moment.
"They are nip and tuck in terms of fitness and will be given until Thursday before we decide if they are ready.
"Geordan didn't train today. He started the game at the weekend for Leicester but had to come off.
"Girvan took part in training today. He did run but he's not there yet. Both are a doubt."
If neither player recovers in time, Rob Kearney will switch to full-back, Tommy Bowe will take the number 11 jersey and Shane Horgan will fill the vacancy on the right wing.