The Blues have made their worst start in their Super Rugby history having lost their first three matches.
A report on Radio Sport said that Tasman ITM Cup coach Kieran Keane had been contacted about replacing Kirwan but the Blues have now denied the story.
Blues chief executive Michael Redman said in a statement that they are "dismayed" at the story and that the "board and management are fully focused on their full support of Kirwan, the staff and team".
The Blues say that no one from their organisation have approached any other coach about Kirwan's position.
"We are dismayed that a media organisation would run this sort of report without attempting to verify its authenticity," said Redman.
Kirwan is contracted to the Blues until the end of the year