Federer is a huge fan of his country's national team and even delivered a morale-boosting pep talk to the players during a poor run of form two years ago.
The 28-year-old was glued to his television as Switzerland claimed a shock 1-0 victory over Spain in their opening World Cup fixture, but a scheduling clash could deny him the chance to see all of the team's second Group H match.
Federer is due on Centre Court at 1200GMT to start the defence of his Wimbledon crown against Colombian Falla, while the Switzerland v Chile tie in South Africa kicks off two hours later.
That gives six-time Wimbledon champion Federer only a short time to win his best of five sets match against Falla and he concedes he might not see the start of the football.
"I'm not going to leave the court when the football starts. Maybe I can install a little screen on Centre Court on the change of ends," Federer joked.
"I still have a chance to go see a little bit. But my focus is always on my first round match here, then I will see how much I can see of the game.
"It's happened in the past that I've had to play matches during important things in my life. Last year I went on court last year many times thinking my wife Mirka was going to give birth to my children. That was much crazier."
Ottmar Hitzfeld's Swiss side haven't lost since Federer spoke to the squad about his experiences of handling the pressure of being a top sportsman following a shock defeat to minnows Luxembourg.
But Federer refused to take any credit for Switzerland's win over Spain, who are one of the big favourites for the World Cup.
"It was nice seeing people in Switzerland going crazy over a win like this. We will talk about this for 20 years. It was amazing," he said.
"When Ottmar Hitzfeld called me and said if I could come in and meet the team, inspire them a bit, answer questions on how I handle the pressure, I said, no problem.
"I came in and I don't think they've lost since. If they give me one percent credit that's great! But they were good enough themselves. They know it. I told them that."