A singles gold medal is the only title missing from Federer's illustrious trophy cabinet that includes, among others, seven Wimbledon titles.
Speaking of Federer, Murray, 25, said: "It's so rare for him to be in a position where he's trying to do something new because he's achieved so much in tennis.
"I hope that will even things out a little bit."
He added: "Most times I've played him, he's experienced the situations way, way more times than me."
Federer will however be used to a Centre Court crowd being against him as he defeated Murray in the Wimbledon final last month.
Crowds at the Olympics have arguably been more partizan than at Wimbledon towards British players and Federer admitted: "I don't know how much the crowd plays in the outcome of the match."
The 30-year-old Swiss has won an Olympic gold in the men's doubles when he and Stanislas Wawrinka were victorious in Beijing four years ago.
Meanwhile, Murray is guaranteed two medals for Great Britain today as he fights with Federer for the singles title before joining forces with Laura Robson to battle for the mixed doubles gold against Victoria Azarenka and Max Mirnyi of Belarus.