Arsenal agreed to let Oxlade-Chamberlain move to Liverpool for £40million after he rejected a deal with Chelsea.
He is currently with the England squad preparing for their World Cup qualifier with Malta on Friday.
But England boss Gareth Southgate has given him permission to have a medical and Sky Sports say confirmation of the move will come on Thursday.
The move will come as a massive blow to Arsenal boss Arsene Wenger, who had been desperate to keep hold of Oxlade-Chamberlain.
Former Red Jamie Carragher admitted he tried to convince Oxlade-Chamberlain to join Liverpool in the past.
“Tried to persuade Alex Oxlade-Chamberlain to join Liverpool when he was a kid, obviously [Jurgen] Klopp is more persuasive,” he wrote on Twitter.
“Interested how he gets him into central midfield after Sunday!”