The striker, who scored 28 goals in all competitions last season, has been linked with a move to the recently-promoted Tigers.
The manager told the Burnley Express: "There's been no agreement reached. The noises are just the same because there's people hovering and clubs interested, but nothing is appropriate for us at this time so he's getting on with pre-season for us.
"There's no reason to think any different until it becomes any different. He's fine, he's in good shape, listening to what we think is appropriate and he's enjoyed himself since coming back for pre-season.
"We're just monitoring it as it unfolds. We want good players in the building and we want to work with good players."
Austin missed the end of last season after undergoing surgery to remove his appendix.