Other names who have been linked with the Republic job include Graeme Souness, Liam Brady, Philippe Troussier, John Aldridge, Finland manager Roy Hodgson, Dutch Under-21 manager Foppe de Haan and former Wigan manager Paul Jewell.
Both Souness and former Japan and South Africa manager Troussier have said that they would be interested in the role.
When question about his prospects on Wednesday, Aldridge said that he had "not given the issue any thought".
Under-21 boss Don Givens will take temporary charge of the senior side for the Republic's final Euro 2008 qualifier against Wales on 17 November.