The Danish holding midfielder arrived at Anfield with a strong reputation but failed to make an impact at Anfield under Roy Hodgson or Kenny Dalglish.
Liverpool have announced they have agreed a deal with Ligue 1 newcomers Evian - for whom the deal would represent something of a coup - and Poulsen can now discuss terms with a view to completing the move.
"Liverpool FC have tonight confirmed that they have reached agreement with Evian Thonon Gaillard for the transfer of Christian Poulsen," said a statement.
"The French side have now been given permission to talk to the Denmark international."
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Source: PA