The Northern Irishman has yet to appoint a deputy for skipper Steven Gerrard since Carragher called time on his career at the end of the 2012-13 campaign.
Rodgers revealed that several members of his squad are under consideration for the role, before stressing the importance of the position on and off the pitch.
"I haven't made it yet; there are a few people that I'm looking at," the boss told Liverpoolfc.com when asked if a vice-captain had been selected.
"The captain and vice-captain is a very important position here at the football club, on and off the field.
"We've got a number of players that I'm looking at and assessing before I'll make that decision at the end of pre-season."
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