Ireland assistant manager linked with position at Sheffield Wednesday but remains committed to Martin O'Neill project
Wednesday owner Milan Mandaric earlier this month suggested that he would make an approach to the FAI for the services of Keane, who only took up the post in time for November's friendly against Latvia.
However, after weeks of speculation, Keane declared that he would not be joining the Owls.
He told members of Castleview AFC in Cork: "I'm staying. We have started something and plan to see it out. In any case, there has been no call made to me. I am in this position now and am happy here and we want to complete the job."
The Championship side currently have Stuart Gray in caretaker charge but his hopes of retaining the post on a permanent basis were hit at the weekend by a 2-1 defeat to Bournemouth.