Federer must wait for the result of Dominic Thiem vs Kei Nishikori to see what he needs to do in the night session.
The Swiss star suffered a shock opening-round defeat against Nishikori before seeing off Thiem in straight sets in round two.
He takes on group leader Kevin Anderson at 8pm tonight, who has won both of his opening matches.
If Nishikori beats Thiem in straight sets this afternoon then Federer is in severe trouble as he must beat in-form Anderson in the same manner, or else he is out.
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However, even if the 20-time Grand Slam winner does record a comfortable victory, progression would then go down to the percentage of games won between those also tied on two wins.
Federer will watch Thiem vs Nishikori closely and if results lean in his favour, he still has the improbable take of getting past Anderson.
"I could win and still not make it, so from that
it's not in my power," Federer said.
"That's okay. If I don't pass, I don't pass, and I deserve not to pass.
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"Important for me is to play a good last match here in the round-robin, try to beat Kevin. He has been playing great. He has had a wonderful season.
"He played great against me as well at Wimbledon. Today he had obviously a good game for him.
"So that's my focus. I can't talk about what would come next because it's a hard match in itself.
"My first-round match here wasn't great, so today was better, and I need to keep that up against Kevin, obviously, if I want to have a chance to stay here in London."
The best scenario for Federer is a Thiem straight-sets victory, as he could then progress even with a defeat, so long as he takes the match the distance.
Federer skipped practice yesterday for a second time this week in a bid to keep his mental welfare in order.
"Important was not about my forehand or my backhand or my serve or anything," Federer added.
"I guess it was my head. For that sometimes you need a break.
"I've been playing a lot of tennis the last two months."