Steve Clarke says Scotland still have a bit of “work to do” as they prepare to face Georgia away in their penultimate Euro 2024 qualifier.
Saturday’s Amsterdam game could be Kenny’s final competitive match in charge with his contract due to expire.
The Republic have lost five of their seven qualifiers with the only wins coming against minnows Gibraltar.
“I think we can [win], there is no reason why we can’t,” insisted O’Shea.
The Republic’s Group B hopes are long over following defeats at home and away by France and Greece, in addition to the reverse in Dublin against the Dutch in September.
In addition, their hopes of earning a play-off based on Uefa’s complicated Nations League rankings now rest of a series of highly unlikely results in other Euro 2024 groups.
Despite that O’Shea, who has recently fought his way back into the Burnley first team, insists the Irish are aiming to upset the Dutch, who are on course to join already qualified table toppers France at next summer’s finals in Germany.
“We know that we cannot qualify, but it is an international game, a competitive game against a great side away and we know we want to do something special as a group,” O’Shea said.
“If that’s all we can do right now, that’s what we want to do – to beat the Netherlands away.
“For ourselves we have ambitions and aims to do well for the country, but also for him [Kenny] – the group loves him. I think we really deserve something like that and he does as well.”
Kenny’s Republic contract will expire after Tuesday’s home friendly against New Zealand although the manager has been deflecting all talk about his future in the run-up to Saturday’s game.
The Republic squad’s emerging star, Brighton striker Evan Ferguson, is among a number of injury doubts for the final qualifier.
Kenny has not specified the precise nature of Ferguson’s issue while the manager revealed on Tuesday that Luton Town winger Chiedozie Ogbene and midfielders Will Smallbone and Jamie McGrath were also fitness concerns.