From Middle High German (Central German) gerüchte, borrowed from Middle Low German geruchte, gerüchte. This northern form replaced earlier Middle High German geruofte, gerüefte, from Old High German geruofti. The noun pertains to the verb rufen (“to call”) (Old High German ruofan, Old Saxon hrōpan). The Low German form is based on the shift -ft- → -cht- (cf. Nichte); the same in Dutch gerucht. Popular etymology later associated the word with riechen (“to smell”).
- Gerücht in Duden online