World number three Federer beat Italian Fabio Fognini 6-4 6-3 in one hour and 13 minutes.

Federer saved two break points when serving at 4-3 up in the second set and, after holding, immediately broke Fognini to love to seal the victory.

Second seed Djokovic reached the last eight after Bosnia's Damir Dzumhur retired with a back injury.

The Serb, 31, who will take the world number one ranking from Rafael Nadal on Monday, was leading 6-1 2-1 when Dzumhur ended the match.

The Wimbledon and US Open champion did not face a break point in the match and won 72% of first-serve points.

He will now face Marin Cilic after the Croat beat Bulgaria's Grigor Dimitrov.

Cilic hit 29 winners as he claimed a 7-6 (7-5) 6-4 victory over ninth seed Dimitrov.

Dimitrov, who won the ATP Finals last year, will finish the season 19th in the rankings in 2018, while Cilic requires one more victory to qualify for this year's event in London.

Djokovic is on a 20-match winning run but was beaten by Cilic in this year's Queen's final.