Federer, defending 1,000 ranking points after winning the title last year, must reach the semi-finals to avoid losing top spot to Rafael Nadal.
Nadal’s latest injury means he isn’t playing but that won’t stop him reclaiming the No 1 ranking if five-time champion Federer bows out before the last four.
The Swiss legend has a simple path through to the quarter-finals, where things potentially get much tougher.
That’s because Tomas Berdych is his likely opponent and, as Federer knows only too well, the Czech world No 19 is no mug.
Indeed, he’s already beaten him six times in the past, including a huge upset on the biggest stage of all, the Wimbledon quarter-finals in 2010 when Federer was the defending champion.
“It’s really tough to explain how I’m feeling,” Berdych told the BBC after his stunning upset win at SW19.
“To play on this stadium against a player as great as Roger and to be standing here as the winner is amazing.
“This was the toughest match of my career to close out, it’s a big step forward and I’m so happy.”
Berdych proved his Wimbledon win was no fluke by dumping Federer out of the US Open quarter-finals two years later.
So there’s hope for Nadal fans that their hero could be back at No 1 without lifting a racket.