Rovers manager Graeme Souness said: "We rejected a third written offer today at lunchtime.
"It did not come up to the requirements we need or the requirements in Duff 's contract.
"That is it unless they come back again. I cannot speak on their behalf on whether they will.
"We have made our case plain that we would like to keep Damien."
Williams, earlier, said: "There is a lot of financial upside to selling which cannot be underestimated in the post-Jack Walker era, but we don't want to sell Duff.
"We know Chelsea can entice Damien with Champions League football but we want him to stay here and achieve that with us."
It is the latest twist in a frenzied fortnight of transfer activity at Stamford Bridge.
Chelsea have already agreed deals for West Ham defender Glen Johnson and Real Madrid midfielder Geremi.
Chelsea, who are at a training camp in Italy this week ahead of Friday's friendly with Lazio, have made an inquiry for Manchester United's Juan Sebastian Veron and been rebuffed in their move for Juventus midfielder Edgar Davids.
