O'Neill is now out of contract with Ireland, meaning that neither Stoke nor the manager himself had to inform the association of discussions.
Former Watford manager Quique Sanchez Flores has also been linked this week but the Potters board will have to negotiate a fee with Spanish side Espanyol given that he is still under contract with them until summer 2019.
Despite O'Neill taking time off for a holiday to reflect, fears of him walking away were allayed by his visit to the FAI headquarters before Christmas to plan for 2018 and attend the association's Christmas party.
"I can't think of any other Association that would allow their manager to stall in this way", Dunphy told News At One on RTÉ Radio 1.
"It's embarrassing for the FAI".
O'Neill's decision in 2016 to delay by five months the signing of his new contract suggested the Derry man had a penchant for working to his pace but this latest prevarication always carried the threat of blowing up in the face of his employers.
It's understood that Stoke have asked Flores for a final answer by this afternoon.
He is held in high regard at the club, with a further pull factor for Stoke the fact that O'Neill has yet to sign the contract he has verbally agreed with the FAI, meaning the club won't have to pay any compensation.
"The FAI now need to explain why having reached an agreement and made an offer, their manager hasn't accepted the offer and was making himself available to other suitors if you like".
Episode 45 of The Hard Yards rugby podcast features an interview with former Munster outhalf Johnny Holland, while James Downey joins us in studio..
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