Ms Cohen told the Mail that she believed Ms Shah had “abused her position” by turning to the police.
“It’s the Corbynistas, if they don’t like someone they try to get them sacked,” she said.
In an added twist Ms Cohen claimed police had told her the spat could be over “jealousy” surrounding another Labour MP, Khalid Mahmood.
Ms Cohen has been Mr Mahmood’s assistant for more than a decade. They were previously in a relationship, but Ms Cohen said they were now “just colleagues”.
She said: “The policewoman who visited me said that Mrs Shah believes I’m jealous of her close relationship with Khalid. I believe they are close friends, but I have nothing to be jealous about.”
Ms Shah has not commented. Mr Mahmood said he could not comment on Ms Cohen’s employment status after it was suggested she may have been suspended from her role.