The football club wants to stop people watching and filming sessions at the Reds' Melwood Drive complex.
Liverpool City Council backed the club's proposals to install 4.5m (15ft) high retractable screens which would be closed during first-team training.
The club said the screens - which will be retracted at all other times - were first planned more than a year ago.
This will minimise the impact on residents, as well as allowing the grass to grow properly.
Liverpool's plans to build high screens around their training ground have been approved by the city council.