whispering campaign 
noun
A systematic circulation of a rumour, typically in order to damage someone’s reputation: his predecessor led a whispering campaign against him...
- The whispering campaign blamed him for damaging the company's relationship with the big brass at the MoD.
- The newspaper story crystallised a whispering campaign against him which seems to have scared off club chairmen who would otherwise find his track record irresistible.
- A long-serving Lib Dem MP, a colleague of Kennedy's for some two decades, said the build-up of rumours bore all the hallmarks of a whispering campaign.