Alvaro Arbeloa and Mohammed Sissoko are both 12/1, with Daniel Agger rated at 14/1 and local lad Jamie Carragher 16/1.
Ladbrokes spokesman Robin Hutchison said: "Liverpool showed at the weekend that they can stand up for themselves and it would be unusual if they went another campaign without someone taking an early bath."
Rafa Benitez's men are even money to last the whole of the 2007/08 league season without having a man dismissed.
Voronin proves top fans' pick
ANDRIY VORONIN is already proving a spectacularly popular signing with Liverpool fans.
The Ukrainian came out on top in a poll conducted by Liverpoolfc.tv asking supporters who impressed them most during pre-season.
Voronin gained a staggering 62% of the votes - the next highest was Jermine Pennant with just 6.6%.