Liverpool are thought to be keen on signing the highly-rated Polish international, but their offer of £4 million is below the Dutch club's £7 million valuation of the player.
Reds boss Gerard Houllier and his assistant Phil Thompson watched Dudek in action last weekend, but he is not thought to be prepared to meet Feyenoord's asking price.
Sander Westerveld's terrible blunder, which gifted Bolton victory on Monday, may persuade Houllier to step up his interest in the shot-stopper before the Champions League deadline this Friday and Feyenoord may be prepared to drop their price by £1 million.
Feyenoord club president Jorien van den Herik wants the situation resolved soon so that he bring in a replacement for Dudek before the Champions League deadline if he finally does leave De Kuip.
"Up until Monday evening I had not received any official bid from Liverpool, despite asking them to do so several times," van den Herik told the club's official website. "I only talked with an agent working for Liverpool who quoted a price of £4 million.
"This offer is the same as that of a few weeks ago when I told them very clearly that our asking price is £6.7 million, although I added that we would be flexible about that price.
"As it is, I fear that we will not reach an agreement and I think that is very sad for Dudek."
Meanwhile, Blackburn Rovers are set to rekindle their interest in long-standing target Liverpool defender Djimi Traore.
Rovers boss Graeme Souness is a big admirer of the Frenchman and would like to bring him to Ewood Park to bolster his defensive options.
Souness has been chasing a new left-sided defender for some time and he has already failed in three previous bids for Traore.
Blackburn's hopes of signing The Reds reserve captain have been boosted by the player's agent Willy McKay's suggestion that he could leave for first team football.
"Djimi wants to play so I think he may be interested if Blackburn were to come back in,"said McKay.
Rovers chief executive John Williams admitted that Traore remained a target they had not given up hope on signing.
"Traore remains a target and we haven't given up on that one yet."
Souness is set to make an improved £4 million bid for the former Laval ace and he hopes it will be enough to persuade Liverpool to sell the highly-rated defender.
