The former Aston Villa and Celtic manager has emerged as the frontrunner for the Ireland job following the departure of Giovanni Trapattoni
Delaney confirmed that businessman Denis O'Brien would continue to provide financial assistance to the FAI "for the next two years at least" as the search begins for the Italian's successor.
"Denis O'Brien has confirmed that he will continue to stick with this project for the next two years at least," Delaney told RTE. "We have the firepower to go to the market to try and get ourselves a manager."
Trapattoni agreed to leave his post as Ireland manager "by mutual consent" after meeting with the FAI in the aftermath of the 1-0 defeat against Austria in Vienna on Tuesday. The 74-year-old, who had been in charge of the Boys in Green for over five years, agreed to a compensation package believed to be in the region of €500,000.
A number of candidates have emerged as contenders to succeed Trapattoni, including former Celtic and Aston Villa manager Martin O'Neill who is currently available.
While the FAI prepare to appoint a new mananger, they have yet to make contact with O'Neill, but the 61-year-old is reported to be interested in the position.
Other names mentioned by John Delaney include Leeds United manager Brian McDermott, Norwich City boss Chris Hughton and former Ireland manager Mick McCarthy, who is now managing Ipswich Town.
Former Ireland international Roy Keane is also among the candidates. The former Sunderland and Ipswich boss is said to be interested in managing his country.