Dossena could make his debut on Sunday at home to Sampdoria.
Out-of-favour striker Andriy Voronin looks set to follow Dossena out of Anfield with a £2m switch to Dynamo Moscow nearing completion.
The Ukranian has scored only five times for the Reds since signing from Bayer Leverkusen in 2007 and spent much of last season on loan at Hertha Berlin.
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