Whisper

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Old English hwisprian, of Germanic origin; related to German wispeln, from the imitative base of whistle.

wiktionary

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From Middle English whisperen, from Old English hwisprian(“to mutter, murmur, whisper”), from Proto-West Germanic *hwisprōn, from Proto-Germanic *hwisprōną(“to hiss, whistle, whisper”), from Proto-Indo-European *ḱweys-, *ḱwey-(“to hiss, whistle, whisper”). Cognate with Dutch wisperen(“to whisper”), German wispern(“to mumble, whisper”). Related also to Danish hviske(“to whisper”), Icelandic hvískra(“to whisper”), Norwegian Bokmål hviske, kviskre(“to whisper”), Norwegian Nynorsk kviskre, kviskra(“to whisper”), Swedish viska(“to whisper”). More at English whistle.

etymonline

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whisper (v.)

Old English hwisprian "speak very softly, murmur" (only in a Northumbrian gloss for Latin murmurare), from Proto-Germanic *hwis- (source also of Middle Dutch wispelen, Old High German hwispalon, German wispeln, wispern, Old Norse hviskra "to whisper"), from PIE *kwei- "to hiss, whistle," imitative. Transitive sense is from 1560s. Related: Whispered; whispering. An alternative verb, now obsolete, was whister (late 14c., from Old English hwæstrian), and Middle English had whistringe grucchere "a slanderer."

whisper (n.)

1590s, from whisper (v.).