Nicola Bulley, a mother of two, went missing on Friday and was last seen on a footpath by the River Wyre in the village of St Michael’s on Wyre.
Her mobile phone, which was still connected to a work call, was found by police on a bench nearby.
Immediately before going missing Ms Bulley, 45, had been walking her springer spaniel who was found loose between the river and the bench.
Lancashire Police have found a man believed to have been in the area at the time Ms Bulley was last seen after they issued an appeal.
Ms Bulley, a mortgage adviser, has lived in Lancashire for 25 years but is originally from near Chelmsford, Essex, and has a southern accent.
She was last seen by a member of the public at about 9.15am, police said.
In a statement Ms Bulley’s family said: “We have been overwhelmed by the support from our community and would like to thank everyone for their ongoing efforts to help us find Nicola. The girls are desperate to have their mummy back home safe with them and your ongoing efforts have provided comfort to them whilst we await news on Nicola.
“We ask for anyone who thinks they may have any information that may help the police find Nicola to please come forward and help them with their inquiries.”
Searches have been carried out by Lancashire Police, using a helicopter, drones and dogs with support from Lancashire Fire and Rescue Service, Bowland Pennine Mountain Rescue team and the North West Underwater Search Team.
Locals have also organised searches in the area.
Anybody with information can call 101, quoting log 473 of January 27, or Crimestoppers anonymously on 0800 555 111.