The Birmingham Mail report that an offer, believed to be in the region of £6m, was made for the 29-year-old as Alex McLeish looked to tie down his long-time strike target but the Cottagers swiftly rebuffed it.
However, as was also the case with Wigan winger Charles N'Zogbia, the Blues are not prepared to be held to ransom and will not be upping their offer for Zamora.
Hull City had a £5m deal lined up for Zamora last summer but the move collapsed over personal terms. The Blues believe his worth has not increased to the extent Fulham feel.