Saracens and Harlequins Irish bosses Mark McCall and Conor O'Shea have both ruled themselves out of coaching Ireland.
McCall and O'Shea have both led their respective sides to Premiership titles in the last two seasons, but have turned down the prospect of coaching the Irish national side.
"It is completely understandable that when jobs like this come up that Mark's name is mentioned because he is one of the most successful coaches in Europe," said Saracens chief executive Edward Griffiths.
"However, just like the rest of our coaching staff, Mark recently signed a two-year extension and he remains totally committed to what we are doing at the club. We have not had any contact from the Irish RFU and our sole focus is the game with Ulster on Saturday."
Harlequins boss Conor O'Shea re-iterated that he would not be applying for the position when asked by the Evening Standard.
"Absolutely not. I am contracted to Harlequins until the end of the 2013-14 season," said O'Shea.
"I will be honouring that commitment and, hopefully, continuing beyond it. Of course with the fixtures this weekend there are lots of questions but I've made my position very clear."