Roger Federer is a 34-year-old father of not one, but two sets of twins, and hasn't been to the finals of the U.S. Open since 2009.

The Swiss Maestro captured the last of his 17 Grand Slam singles titles back at Wimbledon in 2012.

Yet when Federer takes the court on Tuesday in Flushing Meadows for his first-round match against Leonardo Mayer, the No. 2 seed should be brimming with confidence about the chances of capturing his 18th major title during this fortnight.

Federer, who won five straight titles in Queen from 2004-08, is coming off winning the title on hardcourts at the Western & Southern Open in Cincinnati, where he served brilliantly and attacked the net fearlessly en route to beating Andy Murray and Novak Djokovic in back-to-back matches in the semifinals and final. Overall he is 21-2 (.913) with three titles on hardcourts in 2015.

"He played a fantastic week there [in Cincinnati]," Djokovic, the No. 1 seed at the Open, said of Federer. "I still see him as one of the best players in the world, undoubtedly. He’s proven that, he’s No. 2 in the world. He’s played the Wimbledon final. He’s winning big events. He’s still challenging everybody he’s facing on the court. I always see him as one of the favorites everywhere he goes."

Marin Cilic, who crushed Federer in straight sets in the semifinals last year en route to the U.S. championship, agrees.

“Roger is always going to be a contender here and at any Grand Slam,” Cilic said. “I think especially the way he was playing in Cincinnati, I think it’s great for everybody to see.”

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John McEnroe, a four-time U.S. Open champ, wondered Monday on ESPN whether Federer could still bring it for seven matches in a Grand Slam.

"The 34-year-old Federer, he's playing incredible tennis," McEnroe said. "You can see, best-of-3 [sets], he can still beat anybody. The question is seven matches, best-of-5."

Pete Sampras, who won the last of his 14 Grand Slam titles at 31 at the 2002 U.S. Open, believes Federer can still win an 18th major championship. If Federer does so at the Open, he would be the third-oldest man in the Open Era to win a major.

“I think he’s playing well, he’s fit, he hits the ball great, he’s doing everything that he’s been doing for years," Sampras said recently.

“It is tougher as you get older and now Novak and Murray, they’re in their prime now. I think for Roger to win, things need to fall into place. I think if he has to play Murray, Djokovic, then Rafa in one week or back-to-back, it gets more difficult.

“Wimbledon I think is his best chance, but the U.S. Open he’s won there five times, he knows what he’s doing. I think he’s got a good shot, but I think obviously Novak is the man to beat.”

If Federer gets past Mayer, he would face Marcos Baghdatis or Steve Darcis in the second round, with big serving American John Isner and Ivo Karlovic potential Round of 16 opponents. Murray, French Open champion Stan Wawrinka and Tomas Berdych also loom in his half of the draw.

Yet because of a graceful and fluid style of play that makes it seem at times as if he's floating above the court, Federer's game has not taken a heavy toll on his body.

His long-time rival Rafael Nadal, who plays a much more brutish and physical style, appears to be breaking down at the age of 29. Nadal is drawn to meet Djokovic in the quarterfinals here, which could make for a fascinating encounter.

Under the guidance of his coach Stefan Edberg, a serve-and-volleyer who won six majors including the U.S. Open in 1991-92, Federer is attacking the net more late in his career, trying to end the points more quickly, something he needs to do to avoid getting into baseline slugfests with the likes of Murray (his potential semifinal opponent) and Djokovic (his potential rival in the final).

"I had to adjust my game accordingly," Federer said.

"My game’s been going very well. I think my backhand has improved, with having a bigger racket head. .. I think my volleying has been very good and very proactive, going forward, and I think my serve has been unbelievable lately, so it’s clearly very important that that keeps working, because it’s the base of all things. My game is usually great when I move well, which I did well in Cincinnati, so that’s very good going into the Open."

Federer's latest trick in Cincinnati was to stand extremely close to the service line on the opponent's second serve and then rush into the net quickly.

"Credit to him for doing that and figuring out ways to adjust his game and come to the net and win that match," Djokovic said. "That’s what he’s done. He deserved to win in the finals of Cincinnati. No question about it. It’s [up to] me and the others to respond. That is what is so special about the rivalries. We always have taken the best out of each other and make each other improve and evolve as players and get our game to another level."

Whether Federer can take his game to the level he needs to win an 18th major remains to be seen, but the Swiss Maestro certainly has reason to feel confident.

Follow Adam Zagoria on Twitter @AdamZagoria for updates throughout the U.S. Open.