The 23-year-old has been linked with Steve Bruce's promoted Tigers throughout the summer, with some reports claiming a deal was set to go through.
Championship side Burnley have denied that, though, tweeting: "Contrary to media reports, Burnley Football Club has not agreed any deal with Hull City for striker Charlie Austin."
Austin signed for Burnley from Swindon in January 2011 and has scored 45 goals for the club since then, with 28 of them coming last season.
Strike power is something Bruce was short during the 2012/13 campaign, despite his side going up automatically.
Their total of 61 goals scored was amongst the lowest in the division, with midfielder Robert Koren their leading marksman with nine.