Elliott, top scorer in Hull's last 2 seasons, has not been guaranteed a place in their starting line up this season - he has only made the subs' bench in the last 2 games.
However, Hull City chairman Adam Pearson told the Hull Daily Mail "There's nothing happening with the player whatsoever at this stage. There have been no bids or approaches."
The signing of Elliott would be a lucrative one, but funds may limited, despite strong rumours of Alan Maybury being sold to Championship rivals Sunderland.
Irish international Maybury, signed 18 months ago by ex-boss Craig Levein from Hearts, still has 2 years left on his contract. Rumours of his departure fuelled when he was dropped in City's 3-1 home victory against Ipswich Town at the weekend.