The executive described the former Reading boss as a "serious candidate" to succeed Italian tactician Giovanni Trapattoni in the role.
"He is a serious candidate and he is one of the names being mentioned here [on Tuesday] morning," he told BBC Sport.
"I am looking at the names being mentioned and I think it will come down to the three leading the market.
"I am looking at Mick McCarthy and Brian McDermott and I know that both men, having spoken to them over the past couple of years, they would both like to get their hands on this job, not necessarily at this stage."
McDermott, whose parents are Irish, has previously admitted that coaching the national team is his lifelong ambition.
"I know Brian McDermott, given his heritage with his parents being Irish, and having spoken to him on Irish radio, he would love to manage the Republic of Ireland someday," Delaney added.