They have cut the chances of the France striker playing on Merseyside instead of in North London from 10/1 to 3/1.
The decision follows a 48-hour gamble on the transfer going ahead and Hill's spokesman Graham Sharpe told the Daily Mail: "We started to take calls asking for odds for Henry to join Liverpool a couple of days ago and initially offered 10/1, not believing it was that likely a move for the Frenchman.
"However, after taking increasingly more calls and bets - mainly from the Liverpool area - we have shortened the odds significantly just in case there is something to the story, which has yet to emerge into the public domain."
