The 24-year-old has been constantly linked to the Spanish giants over the past few summers, but the transfer saga appeared to be coming to a close after Barcelona offered a reported £26m for the midfielder.
Despite the initial bid, Hill-Wood believes that the European champions need to act fast if they are going to land the Spanish international.
"They have been messing about for a year and a half now and they have got to make up their minds," the Daily Star quotes the chairman as saying.
"The ball is in their court. They have made one bid of around £26m and another rather tentative one.
"If they want to buy the player they are going to have to pay the right price - and when you look at what is being paid elsewhere I don't think what we are asking is at all unreasonable."
The Premier League side are reportedly looking for a fee in the region of £40m for Fabregas.