The detective leading the investigation into the disappearance of Claudia Lawrence said he had received 40 calls following a television appeal for information about the chef's relationships "of complexity and mystery".
Det Supt Ray Galloway, of North Yorkshire Police, told BBC1's Crimewatch programme he was certain Miss Lawrence had not told her family or friends about some of her relationships.
The 35-year-old was last seen near her home in York on 18 March and did not arrive for a 6am shift at work the following morning.
North Yorkshire Police have now formally classified the investigation into her disappearance as one of suspected murder.
Last night, nearly 11 weeks since Miss Lawrence went missing, a Crimewatch appeal showed reconstructions of her last known movements and interviews with her father, sister and closest friend.
After the programme, Mr Galloway said he had received calls with information about Miss Lawrence's relationships as a result of the appeal.
He said: "We have had information and callers who have either been in a relationship with Claudia, or suspect other people have been in a relationship with Claudia."
The detective said he would trace anyone who had been involved in a relationship with Miss Lawrence and urged those people to come forward now.
"We have information and if people want us to deal with them in a controlled, a confidential, in a discreet way then the opportunity is now," he said.
"They need to call us now and impart the information they have."
The programme also featured previously unseen footage of the inside of the University of York chef's house on Heworth Road and home video footage of her as a child.
Speaking on the programme, Mr Galloway appealed for anyone who had been involved in a relationship with Miss Lawrence to come forward.
He said: "As the investigation has developed, it's apparent that some of Claudia's relationships had an element of complexity and mystery to them.
"I am certain that some of those relationships were not known to her family or her friends.
"I need to know the details of those relationships, in fact I do know the details of some of them, and I would urge anybody that was involved in a relationship with Claudia, or knew of one that a friend, a colleague, a neighbour was involved in, please, if they're going to be discreet and if they want to actually enable us to deal with it in a controlled way, a confidential way, they need to pick up that phone."
Mr Galloway continued: "I'm not here to judge Claudia's relationships, I'm here to investigate them. I need people to share that information with me."
Miss Lawrence's friends and family have previously dismissed speculation that she may have had a secret boyfriend.
Last night's programme also saw Miss Lawrence's sister, Alexandria Sims, give her first interview in relation to the chef's disappearance.
Mrs Sims said: "I find it hard to accept that people just vanish into thin air.
"There must be people out there that have seen something suspicious or who know something that's happened."
She continued: "There's frustration at not knowing what's happened to her because obviously someone must know what's happened and someone must know someone else who knows what happened."
Their father, 62-year-old solicitor Peter Lawrence, added: "It's almost unbearable not knowing and if anyone else out there who does have the knowledge has a family, they must know what we're going through."
The programme also featured reconstructions showing sightings of people police are trying to identify.
One witness reported seeing a couple on Melrosegate Bridge at around 5.35am on the morning of March 19, while another saw a man and a woman arguing near the university half an hour later.
Police have also released CCTV footage of a man seen near Miss Lawrence's home the same morning.
Mr Galloway renewed his appeal for these people to come forward.
The investigation into Miss Lawrence's disappearance is the biggest North Yorkshire Police have conducted since the search for multiple killer Mark Hobson five years ago.
Crimestoppers have offered a £10,000 reward for information leading to the conviction of those responsible.
Police said they had received around 40 calls offering information since the Crimewatch programme.
A spokesman said callers had contacted the Crimestoppers charity, Crimewatch and North Yorkshire Police direct.