Federer played Murray in a charity exhibition in Scotland a week ago. It was Murray's first event since Wimbledon, where the 30-year-old was affected by a hip injury.
Murray took a set off Federer and showed improved movement during their friendly encounter.
"I think in some ways it was a brave move for him to just put himself there, give it a go. Nobody really knew how he was doing," said Federer at this week's ATP Tour Finals." It would have been easy for him to just say, 'You know what, I'll have somebody else play.'
"I think the fans were excited to see Andy play. He got great support, which I was happy to see in my rival's home country. To see him getting this much support was beautiful."
Murray had been back on the practice court for just a couple of weeks, and aims to return for the Australian Open. While saying a lot would depend on the level Murray wants to be at before returning to competition, Federer offered a positive assessment of his opponent.
"I was actually happy how he was playing. Definitely he can move better, he can serve better," said Federer. "For a start, I think it was actually quite encouraging and actually okay. He still has a lot of time before Australia comes around. But I thought he was actually pretty good. I didn't expect him to be this good, yet."