The departure of Declan Kidney from a post he has held since 2008 moved a step closer with Sunday's 12-8 RBS 6 Nations defeat by Scotland, and it is unlikely his contract will be renewed when it expires this summer.
O'Shea had been installed as the favourite to succeed Kidney, who is facing calls for his removal from supporters and pundits, but the 42-year-old said: "I'm contracted to Harlequins until the end of the 2013-14 season. I will be honouring that commitment and hopefully continuing beyond it."
Since winning the Grand Slam in 2009 in his first Six Nations as head coach, Ireland's fortunes have fluctuated wildly under Kidney with their quarter-final defeat by Wales at the World Cup two years ago their lowest ebb.
The current championship began with a promising victory over Wales in Cardiff, but subsequent defeats to England and Scotland have raised grave concerns over their tactics, leadership and execution.
Kidney has been criticised for relieving Brian O'Driscoll of the captaincy in favour of Jamie Heaslip before the Six Nations began, with the Leinster number eight struggling in the role.
The choice of Paddy Jackson ahead of Ronan O'Gara, Ireland's most capped player, as the replacement for hamstring injury victim Jonathan Sexton at Murrayfield was also condemned.
While Jackson made a solid debut in open play, he missed eight points from the kicking tee, a critical number in a four-point defeat. However, O'Gara's poor form hardly warranted his selection.
Ireland have been depleted by injury and suspension - they were missing seven guaranteed starters in Edinburgh - but even allowing for their absentees, their performances against England and Scotland were dismal.
The Irish Rugby Football Union have remained silent to date, but it is hard to envisage Kidney continuing as head coach beyond the Six Nations, even if France and Italy are dispatched in the remaining two games. Behind O'Shea in the bookmakers' running is Ireland Under-20 coach Mike Ruddock, the former Wales boss, and Leinster's Joe Schmidt.