The 30-year-old Croatia international was held for questioning by police last week before he was released pending further inquiries.
He was ordered to answer bail on Monday, which has now been extended to February 1 next year.
Police were called to an apartment in Manchester city centre in the early hours of last Monday, October 25, when the allegation was made.
Klasnic was not at the address when the complaint was made and was arrested some time later, sources said last week.
A Greater Manchester Police spokesman said: "A 30-year-old man arrested on suspicion of rape has been re-bailed until February 1 pending further inquiries."