The 32-year-old Barcelona midfielder has fallen down the pecking order at the Nou Camp this season since the signing of Cesc Fabregas and the emergence of Thiago Alcantara, and the club are willing to let him leave.
The Reds have been heavily linked with the Mali international, with manager Kenny Dalglish keen to bolster his midfield ranks, and Keita has refused to rule out a move.
'A challenge elsewhere would appeal to me, and Liverpool are a great team with great players,' he said.