According to reports emerging from the United Kingdom overnight Albion coach Nigel Clough confirmed the Australian is in talks with Hull.
Irvine was left out of Burton Albion's 1-1 draw Sheffield Wednesday on Saturday, with Clough saying post-match he expects a deal to be done soon.
"I think there's interest and there's a deal being discussed at the moment. Nothing is concluded. It wasn't right to involve him today," Clough told Burton Mail.
When pressed on if he expected the deal to be done, Clough said: "Yes we do, but you never know until it's actually signed."
Irvine, 24, will now head to Tokyo to link up with the Socceroos ahead of their crucial FIFA World Cup qualifier against Japan on Thursday night.
The Melbourne-born midfielder was one of Burton Albion's best performers last season, scoring 10 crucial goals as they managed to avoid relegation by a single point last season.
Hull were relegated from the Premier League last season and currently sit in eighth position, with hopes of returning to the English top flight for a fourth time in ten years.