Giovanni Trapattoni parted company with Ireland last month after five-and-a-half years in charge and Under-21s boss Noel King has taken charge for the remaining World Cup qualifiers against Germany and Kazakhstan.
Ruud Dokter, the Football Association of Ireland's high performance director, and former international Ray Houghton have started the search for a successor and a number of candidates have been sounded out.
"We are doing it together," said the Dutchman.
"There has been a lot of interest and yes, we have talked to some people, and that's actually all I want to say about it because it's an ongoing process."
Asked if that process could take some time, Dokter replied: "Yes."
Martin O'Neill has been installed as favourite to replace Trapattoni, while Gerard Houllier has also been linked with the role, but Dokter gave brief details about what he was looking for in a candidate.
"A good manager for the senior team. That's all I want to say about it," he said.