O’Shea was immediately installed as the favourite to succeed O’Connor after the Australian left Leinster by mutual consent on Thursday morning.
But it is understood that O’Shea has no intention of walking away from Harlequins and intends to honour his contract, which expires next summer.
O’Shea has persuaded his senior players – such as England captain Chris Robshaw, Mike Brown and Joe Marler – to remain faithful to the club and believes he would be letting them down if he broke his contract.
And despite failure to qualify for the European Champions Cup, the 44-year-old is also thought to be excited by Harlequins’ prospects next season, with Jamie Roberts, Adam Jones and Tim Visser all joining the club over the summer.
O’Shea came through the ranks at Leinster, scoring the province’s first ever try in European rugby back in 1995, as well as winning 35 caps at full-back for Ireland in a stellar playing career that was cut short by injury.
But despite his strong personal links to the province it is thought highly unlikely that O’Shea would entertain an approach for his services if one were made.