The 20-year old Australian midfielder is unlikely to see a regular amount of game time with the Scottish champions this season and is wanted by Killie boss Allan Johnston for a six-month spell.
"Jackson Irvine is definitely one we are interested in but nothing has been sorted out yet," he said.
"It's a tough decision whether to go on loan or not," he told The Sun. "My priority is to be a Celtic player, this is where I want to be.
"It's going to be very hard to break in there. Going on loan for six months wouldn't do me any harm - it would give me a chance to step up and play regularly."