If the Swiss player beats Robin Haase on Friday he will usurp Rafael Nadal in the ATP rankings.
Roger Federer one win away from historic world No 1 spot
Roger Federer is a victory away from becoming the oldest world number one in tennis history.
The Australian Open champion is through to the ABN AMRO World Tennis Tournament quarter-finals, although he was made to sweat by Philipp Kohlschreiber.
The German forced the first set in Rotterdam to a tie-break, which Federer won before taking the match 7-6, 7-5.
Victory in the quarter-finals against Dutchman Robin Haase, who beat compatriot and wild card Tallon Griekspoor, would see the 36-year-old Swiss usurp Rafael Nadal at the top of the men's game.
Not only would it take him back to the top of the ATP Rankings for the first time in more than five years, but Federer would comfortably replace Andre Agassi as the oldest number one. The American was 33 when he was last on top in September 2003.
Meanwhile, second seed Grigor Dimitrov beat Filip Krajinovic 7-6 (7/4) 7-5 to set up a meeting with Andrey Rublev, who defeated Damir Dzumhur 6-4 7-6 (7/4).
Daniil Medvedev secured a comeback win against Pierre-Hugues Herbert to secure a clash with Andreas Seppi on Friday.