Lisa Blunt, 23, vanished after leaving her Nottingham home for a last- minute shopping trip on 22 December.
Police said her partner, Vincent Shilton, 29, was being voluntarily questioned by detectives looking for Ms Blunt. Officers have also been searching the couple's home and garden in Raymede Close, Bestwood, Nottingham, where neighbours said it was would have been out of character for her to leave her children before Christmas.
Ms Blunt has lived at the address for three years after moving from the Clifton Estate, on the other side of the city.
Neighbours said Mr Shilton moved into the three-bedroomed semi 18 months ago and the couple had a baby daughter, Kylie, in June this year. It is thought that he left his wife and their three children after meeting Ms Blunt in early 1996.
Ms Blunt's children, Jade, aged five, Dale, four, Daniel, two, and baby Kylie, are being cared for by relatives.
Neighbour Patricia Johnson said Ms Blunt was "devoted to her children" but added that she had become withdrawn in recent months.
"We thought she might have post-natal depression ... I saw her on the Friday before Christmas and she looked really down in the dumps ... We get more worried as time goes on. Now we hope that she has got post-natal depression and that she will come back.
Mr Shilton appealed yesterday for Ms Blunt to get in touch. "We just want to know you are all right," he said.
A Nottinghamshire police spokesman stressed that Mr Shilton had not been arrested and had given his permission for a "thorough examination" of the house and garden.
He added that they were "increasingly concerned" because Ms Blunt had now missed Christmas and her son Dale's fourth birthday on Monday.