The prolific striker has been linked with a possible move to the Bhoys as a potential replacement for Norwich target Gary Hooper.
Celtic assistant manager Johan Mjallby has admitted Austin would be on their list of targets should Hooper leave with the 23-year-old one of the hottest properties in the UK.
The former Swindon forward has scored 23 goals this season after netting 17 last term, and his form has not gone unnoticed by several Premier League clubs.
Austin's representative, David Threlfall, admits he would not be surprised if other clubs were looking at the striker, but cooled the rumours surrounding the Burnley hot-shot.
"There is always going to be interest in someone like Charlie, but while speculation is always flattering, Charlie is fully focused on doing his best for Burnley right now," Threlfall told Sky Sports.