enlarge Detective Superintendent Ray Galloway was speaking two years after Miss Lawrence was last spotted on a CCTV camera near her home in York and had contact with her family.
The chef, who would now be 37, was last seen on March 18, 2009 near her home in Heworth, York. She never turned up for work the next morning in the kitchen at York University.
North Yorkshire Police launched a huge inquiry which has subsequently been scaled back.
Detectives have said repeatedly they believe Miss Lawrence has been murdered and that the key to the inquiry is her relationships with a number of men - relationships police have described as having an "element of complexity and mystery to them".
Asked if it was possible that he could have spoken to Miss Lawrence's killer as part of his inquiries into her past, Mr Galloway said: "There is a real potential that we have."
He said there were no specific suspects, but he said there were individuals he needed more information about and he appealed for people who had concerns or suspicions about someone to come forward.
"I have a knowledge and understanding and context of Claudia's life and her relationships," the detective said.
"I just need somebody to make sense of elements of that information. Certain people I need further information about."
Commenting on the lengthy investigation, he added: "It haunts me. I think about Claudia. I think about the investigation day in, day out.
"I think people expect me to continue working. I work on behalf of Claudia's family and on behalf of the greater community. Until Claudia's killer is brought to justice there is a danger and we need to resolve it.
"I'm amazed by the fact the public's interest and support of the investigation is undiminished."
Mr Galloway said he still received letters from the general public.
He said his team of officers was no longer working full-time on the investigation but he said he still had officers and resources available should he need to act.
He added that there was "no proof of life" but it "would be the best birthday present if Claudia was to walk through the door, but I think it is unlikely".
Earlier this week, Miss Lawrence's mother, Joan, said she believed her daughter was still alive.
"My instinct tells me that she's still alive," she said.
But she added that she believed there had been an "awful lot of mistakes" in the inquiry, pointing particularly to "all this talk of old boyfriends".
"It's not the Claudia I know," she said.
The campaign to find Miss Lawrence has been spearheaded by her solicitor father, Peter, who is divorced from her mother.
Mr Lawrence spoke of his family's anguish as he visited York University today.
He said: "Being here is obviously an extremely poignant occasion for me, particularly because today is two years to the day since Claudia disappeared and two years to the day since I went to her house in Heworth.
"She has obviously not been seen since. No one has heard from her and we still do not know what happened to her.
"The family are obviously distraught by this and have been for the past two years. It doesn't get any easier as time goes on. In fact, in some ways it gets worse because of the length of time of not knowing what has happened to Claudia.
"I have said continuously throughout the past two years there is someone out there who does know what happened to Claudia, there's someone out there who knows a member of their family or a neighbour or a workmate or a friend who they know has some information about Claudia's disappearance."
Mr Lawrence said "if they have any conscience at all", they must come forward.
"They must know what we are going through and we really do need to be put out of this anguish which has plagued the family for the past two years."
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