Delaney, who has presided over stringent cutbacks which have affected even Republic of Ireland boss Giovanni Trapattoni and his coaching staff, reportedly earns around 340,000 euros a year.
However, he has revealed he could have left for a better-paid position and believes his wage is commensurate with the FAI's income, with Ireland still in the grip of a difficult economic situation.
Delaney told Sky Sports News: "I was offered a job three times the salary that I'm currently on, and that's a fact.
"I didn't take the job, I didn't want the job. I'm very happy in this job.
"I think the turnover of the FAI in the mid-90s, 1996,97, was about seven million euros. Last year it was north of 40 million euros.
"We are in a tough economy here in Ireland at the moment and anybody who is on a big salary is going to grab media attention."
Delaney also defended the FAI against accusations from Northern Ireland manager Michael O'Neill that they have poached players born in the North to represent the Republic.
He said: "The way I look upon it is we have never asked anyone to play for us who didn't want to play for us, so the players come and declare.
"That can be historic roots too - players like James McClean and Darron Gibson from Derry, they want to play for the Republic of Ireland, that's what they want to do.
"They may have played underage football for the North - and I'm respectful of that - but ultimately it comes down to the players' choice."
However, Delaney admits he would happy to see a team one day representing the whole of Ireland, as their rugby union colleagues do.
He said: "That's something I would personally like to see.
"I think anything like that is inextricably linked to a solution for the whole island. I don't think that can happen aside of that."