Pressure has increased on the coach in the wake of another poor performance in the Six Nations at the weekend, which saw the Irish dominate play against Scotland at Murrayfield before losing the game 12-8, effectively ending their hopes of winning the competition.
Kidney's contract runs out at the end of the Six Nations and it is widely anticipated that it will not be renewed, but his former captain says the players still have full confidence in him.
"Yeah, absolutely," Brian O'Driscoll told TV3.
"And it is not just Declan, it is the whole coaching staff. Declan heads everything but there is big confidence in the work that is being done. Our discipline has let us down in the last couple of game and we need to reassess that and look at one another."
Since winning the Grand Slam in his first Six Nations as coach in 2009, the Irish have seen mixed results under Kidney.
This year's championship started well with a promising win over Wales in Cardiff, but losses to England and Scotland have raised concerns over tactics.
Kidney has been criticised for relieving Brian O'Driscoll of the captaincy in favour of Jamie Heaslip, with the Leinster player seeming to struggle in the role, while the choice of Paddy Jackson ahead of Ronan O'Gara has also been questioned after the Ulsterman missed eight points from the kicking tee during Sunday's shock defeat in Scotland.
O'Driscoll, who called the most recent loss "frustrating", said it is not for him to comment on whether Kidney's contract should be renewed.
He said: "It is definitely not for me to make a decision on. Firstly it is not my call and secondly I don't know whether I am going to be involved or not, and if we start looking beyond Six Nations at this point we are going to fall another couple of times."