Alisson has been absent since suffering a calf injury during the Premier League opener at home to Norwich City on August 9.
The Brazil international returned to full training earlier this month and has spent extra time at Melwood during the international break working with goalkeeping coach John Achterberg.
The impressive form of stand-in Adrian has meant Liverpool have been under no pressure to rush Alisson's return.
But with the goalkeeper now back to full fitness, he is primed to feature at Old Trafford on Sunday as Jürgen Klopp's Premier League leaders aim for a record-equalling 18th successive top-flight victory.