The Swiss maestro, who last held the top ranking in November 2012, will return to the summit if he reaches the semi-finals at the ATP 500 event.
After seeing off Ruben Bemelmans in the first round, two-time champion Federer came through 7-6 (10-8) 7-5 against Philipp Kohlschreiber in a hard-fought battle on Thursday.
That secured his place in the last eight, before Haase overcame fellow Dutchman Tallon Griekspoor 6-4 6-0, fighting back from a break down in the opener and rescuing three break points in the first game of the second before cruising through.
