Nev Kemp, 48, had been organising a meeting with sergeant Rachael Johnson, 38, over the phone, when her husband Ross, 40, overheard the exchange, a source told The Sun.
Mr Johnson, also a police sergeant, then reported Mr Kemp to other senior officers at Surrey Police.
An outside force has now been brought in to assess the complaint. Mrs Johnson is said to have claimed she was vulnerable following the death of a relative.
A source claimed: ‘Rachael and the deputy chief constable worked closely together. One thing has seemingly led to another.’
Mr Kemp joined Surrey Police in 2017, before taking over over from former-deputy chief constable Jeremy Burton.
Mr Burton stepped down over allegations he had an ‘inappropriate relationship’ with a colleague in February.
A spokesperson for Surrey Police confirmed they are aware of the complaint relating to Mr Kemp and said the matter was in its ‘very early stages’.
They went on: ‘It has been allocated to another force Professional Standards Department to assess.
‘Whilst we await the outcome of this assessment it would not be appropriate to comment further.’