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The England international has been identified as an important potential addition to Jürgen Klopp’s squad and would be a replacement for Sadio Mané when he plays for Senegal in the Africa Cup of Nations next month.
Oxlade-Chamberlain would be expected to command a fee of between £20m to £25m, it is believed, and has just one more year left on his contract at Arsenal after this campaign.
The 23-year-old has been given glowing references of the way Klopp works by fellow internationals Jordan Henderson and Adam Lallana while away with England.
Oxlade-Chamberlain has scored six goals, and provided six assists, for Arsenal this season – his most productive return for the club – but is yet to complete 90 minutes.
It is understood he is frustrated at not being given the chance to establish a regular place in the team.
The midfielder, who joined Arsenal from Southampton in 2011 for an initial fee of £12m, is popular with the Arsenal supporters and would be torn about the prospect of leaving.
However, a move to Liverpool would be tempting not least because he is yet to discuss a new deal at Arsenal.
Oxlade-Chamberlain is one of several Arsenal players – headed by Alexis Sánchez and Mesut Özil – with less than two years left on their contracts and, while manager Arsène Wenger has indicated that talks will take place there is no agreement yet.
Liverpool Manager is keen to buy in January, and also interest in winger Christian Pulisic but Borussia Dortmund have said they will not sell.