Federer will meet Japan's Kei Nishikori in the last eight after his 6-4 6-4 victory over Kevin Anderson.
"I think the first game was everything today".
"I feel like it's better for me to play matches rather than practice", Federer said.
"I am very close to London, to securing my spot mathematically", Cilic said. I really don't want that.
"It's always fun to play him".
He beat Djokovic here at the equivalent stage two years ago and also at this year's Queen's final before Wimbledon.More news: Trump Tries To Revive Doubt Over Kavanaugh Claims After Little-Known Accuser Recants
Nadal, who has not played since a knee injury curtailed his US Open campaign in the semi-finals, pulled out of the final tournament of the regular season due to an abdominal injury.
Djokovic established his quarterfinal clash with fifth-seeded Marin Cilic.
The Serb, who learned on Wednesday that he would be back as world number one next week following Rafa Nadal's withdrawal from the tournament through injury, was leading 6-1, 2-1 when the Bosnian submitted to a back problem that had flared up in the first set.
"My objective is London".
The Spaniard, for all his success at Roland Garros, has never lifted the trophy at the Paris Masters - his best showing came when he lost the 2007 final to David Nalbandian. "But I'm not there yet".
A fresh Federer made the most of his rest to storm into the lead against the wasteful Fognini, who could not subsequently capitalise when his opponent's performance levels dipped at the end of either set.
"It's out of my hands", Barty said in her post-match press conference.More news: Novak Djokovic and Roger Federer to meet in mouth-watering Paris semi-final
"I just go day by day, no? It was a lot of luck".
The Paris Masters coverage gets back underway on Sky Sports Main Arena (409) at 6.30pm, just before Federer is set to take to the court.
But Federer, who got through a few hard situations last week on his way to winning the Swiss Indoors for the ninth time, saved both and then held to clinch the first set.
Federer was given a standing ovation after his win. "The atmosphere was wonderful".
Djokovic revealed he also was not feeling very well out on court.
Dzumhur had a lengthy massage on his lower back late in the first set.
Despite saving three match points before triumphing the tie-break 11-9 in the second set, the American serving machine failed to repeat that in the decider as the Russian sealed the win at 10-8.More news: President-Elect of Brazil Plans to Close Palestinian Embassy
Djokovic will be unveiled as the new No. 1 on Monday when the ATP rankings are released. "I tried. It's good to play in a relaxed manner for once, to find something in my game that could help me out for London", he said.