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The 25-year-old midfielder, who missed yesterday's opening fixture of the 2005/06 campaign due to a thigh injury, handed in his request following the departure of Steve Claridge but acting chairman Theo Paphitis is in no rush to sell.
"Livers asked to go on the transfer list and that hasn't changed," Paphitis told the club's website.
"We've had enquiries from two clubs, but neither have matched our valuation.
"We would dearly love Dave to stay at Millwall, but his contract is up at the end of the season when he would be in a position to leave us for nothing."
Paphitis continued: "We signed Livers for £30,000 from Arsenal and they have a 30% sell-on clause should he leave us, so any offer we receive has to be worthwhile for us."
Manager Colin Lee has also siad that Livermore will still be considered for tomorrow night's game against Coventry City should he shake off his injury in time.
"As far as I'm aware, he will still be at the club for the Coventry game." said Lee.