The sides meet at Aviva Stadium in round four in what is being billed as a Guinness Six Nations championship decider.
Number eight Doris suffered a knee injury against Scotland on 9 February, while hooker Kelleher picked up a neck injury in the same game.
Doris' replacement for the win over Wales in round three, Jack Conan, is expected to recover from a back injury that saw him replaced at the start of the second half in Cardiff.
Prop Furlong has been struggling with an issue relating to his calf and hamstring, playing just once for Leinster in the Champions Cup in January since mid-October.
Utility back Ciarán Frawley, who suffered a head injury in the Ireland A fixture against England A eight days ago, is on course to be available.
Max Deegan, Darragh Murray, Tommy O’Brien and Tom O’Toole have all been added to the squad after also featuring in that game.
"Ireland captain Caelan Doris continues to make positive strides and it is hoped that he will be available for selection alongside Jack Conan," said the IRFU.
"Tadhg Furlong will continue his rehabilitation this week with a decision on his availability, as well as Rónan Kelleher, will be made later in the week.
"Ciaran Frawley is on course to return following his recent concussion."
The Ireland team will be named at lunchtime on Thursday.
Elsewhere, Scotland head coach Gregor Townsend has called up Matt Currie, Ben Muncaster and Nathan McBeth for Saturday's clash with Wales but Luke Crosbie and Jack Mann have been ruled out by injury.
Currie has been recalled after scoring a hat-trick for Edinburgh against Munster on Friday night having recovered from concussion.
