Liverpool goalkeeper Alisson has remained at Melwood for the international break in an attempt to be fit for the Manchester United clash.
The Brazilian goalkeeper has been sidelined since picking up a calf injury in the opening match of the season against Norwich.
Adrian has filled in for the Liverpool No.1 and the performances of the ex-West Ham man have allowed Alisson to be eased back into action.
ESPN reports Adam Lallana and Alex Oxlade-Chamberlain have also decided to do additional training over the next week.
The pair have struggled for regular action after their respective injuries but are now back in Klopp's first-team plans.
