The Scot, who took just over two hours to beat Alexander Zverev in the opening round, hurried to check his phone to see whether there were any messages from home.
“I’m looking forward to any news because I just came off the court,” he said in an on-court interview.
“I’m hoping my phone hasn’t been buzzing in my bag. Kim will message my team if anything goes on and we’ll see what happens.”
Murray has pledged to quit the Australian Open if his wife Kim Sears, who is due to give birth next month, goes into labour — even if it means missing the final.