Roads have been closed along the River Wyre in St Michaels on Wyre, Lancashire.
It has been the focus of an intensive search since Ms Bulley, 45, was last seen walking her dog around 9.10 a.m. on January 27.
Officers said the mother-of-two had fallen into the river, but her friends and family said there was “no evidence whatsoever” to support that theory.
Police said she had suffered “significant issues with alcohol” which had been brought on by “ongoing struggles with the menopause”.
But Ms Bulley’s family said they were “aware beforehand that Lancashire Police released a statement with some personal details about our Nikki.
“Although we know Nikki would not have wanted this, there are people out there speculating and threatening to sell stories about her,” they said in a statement. This is abhorrent and must be stopped.
“The public’s attention must be focused on finding her, not on making up wild theories about her personal life.”
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The dog walker who discovered Nicola Bulley’s phone on a bench told Sky News that he thought “this is not right” when he saw it the morning of her disappearance.
The man, who identified himself as Ron, also stated that he saw the phone wallpaper depicting Ms Bulley and her partner, Paul Ansell, before police were called and she was reported missing.
He claimed to have given the police a detailed statement.
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