"unsubstantiated report, gossip, hearsay;" also "tidings, news, a current report with or without foundation," late 14c., from Old French rumor "commotion, widespread noise or report" (Modern French rumeur), from Latin rumorem (nominative rumor) "noise, clamor; common talk, hearsay, popular opinion," which is related to ravus "hoarse" (from PIE *reu- "to bellow").
Dutch rumoer, German Rumor are from French. The sense of "loud protest, clamor, outcry" also was borrowed in Middle English but is now archaic or poetic. Also compare rumorous "making a loud, confused sound" (1540s). Rumor-monger is by 1884 (earlier in that sense was rumorer, c. 1600). The figurative rumor mill is by 1887.
1590s, transitive, "spread a rumor; tell by way of report," from rumor (n.). Related: Rumored; rumoring.