The Lithuanian, 22, who came through three qualifying rounds to reach the main draw of the Melbourne event, beat 25th seed Florian Meyer in the second round.
"I practised with him before the Australian Open last year, before he started qualifying, and again in Brisbane [a few weeks ago]," said Murray.
"He works hard, he's a really nice guy and it's nice to see him do well because we spent quite a bit of time practising together.
"He is a very hard worker, he has had a couple of injuries over the last couple of years and it will be tough."
Berankis is currently ranked 110th in the ATP rankings.