Next up for the 17-time grand slam winner is Australian rising star Bernard Tomic, who Federer beat in the fourth round of last year's tournament.
"I think there's always excitement about Aussies playing here," Federer, 31, told reporters. "I played him here last year. The crowd was great. I played him in Davis Cup. Crowds were fair there, too. I expect something similar.
"Hopefully we're going to live up to the expectations and live up to the match. Hopefully it's not going to be a bad match. I don't want that to happen."
Murray was beaten by Federer in the 2010 final, but having clinched his first grand slam title at last year's U.S. Open the Briton will be hoping to win in Melbourne having twice been a runner-up.
He set up a third round encounter with Lithuania's Ricardas Berankis after a comfortable 6-2 6-2 6-4 win against Portugal's Joao Sousa.
Sixth seed Juan Martin del Potro eased past German Benjamin Becker 6-2 6-4 6-2, while French seventh seed Jo-Wilfried Tsonga battled to a straight-sets win over Japan's Go Soeda.
Meanwhile, former world No. 1 Rafael Nadal will make his long-awaited return to action at the Chile Open in Vina del Mar early next month.
Spain's 11-time grand slam winner has not played since injuring his knee at Wimbledon last June, and had to delay his planned comeback in Melbourne after suffering an illness in December.
Nadal will also play in another South American clay-court tournament, the Brazil Open starting on Feb. 11, as he seeks to regain fitness ahead of his French Open title defense.