The world No. 1 stepped up his preparations at the Western & Southern Financial Group Masters this week, looking to hone his game before he bids to win his sixth consecutive U.S. Open title and claim a 16th Grand Slam crown.
Murray lost to Federer in the final in New York last year, but the Swiss said there were plenty of other players who could be just as dangerous.
"If you look at last week's draw [in Montreal], so many guys are very equal, I think, right now," Federer said. "The final was close, for instance. I think there are many guys who are beating each other right now so it's quite an interesting dynamic.
"We all know Rafa [Nadal] was injured, so he couldn't put in the fight he wished to concerning the rankings. Now he's back, I'm back playing again after a few weeks. Everybody seems healthy again, and that can only be a good thing for the rest of the season. I'm sure Nadal will bounce back strong if he's really fit and healthy," he said.
Murray, who won the Rogers Cup on Sunday, leapfrogged Nadal to become the first Brit to be ranked No. 2.
Federer admitted that the 22-year-old had become a force on hard courts through his results in the past 12 months.
"I think [Murray] announced himself when he won here last year," Federer said. "From then on he had an unbelievable run, especially on the hard courts. He's almost won everything there is to win ... he's done really well so it doesn't come as a surprise to many people now."
In Federer's first event since winning Wimbledon and since wife Mirka gave birth to twin girls last month, he was beaten in the quarterfinals in Montreal by Frenchman Jo-Wilfried Tsonga having led 5-1 in the final set.
Nevertheless, the 28-year-old said he was happy with his game, even if he will not be putting too much pressure on himself to do well this week.
"It would be good [to do well], but it's not crucial," he said. "I'm going to try everything to have a good tournament here. This tournament has been tricky for me. Either I won or I lost early. I hope it's one of those years where I can go all the way again.
"I feel my game is good enough to do really well here," he said. "Then again, I still have to do little adjustments playing on hard courts again. I'm very excited to be [heading] back to New York."