North Yorkshire Police confirmed that after two years of work, DNA analysis, which was the one remaining line of inquiry, had not yielded any suspects.
The senior investigating officer in the case Detective Superintendent Dai Malyn said Claudia's family had been updated and remain "desperate for a break-through."
The disappearance of the 35-year-old chef in 2009 sparked one of Britain’s biggest missing persons inquiries.
A team has used the national police database to look for DNA profiles similar to multiple unidentified samples recovered during the investigation, including a partial DNA profile found on a cigarette from Miss Lawrence’s car.
People with similar DNA profiles were visited and their family trees were researched to see if there was anyone possibly linked to the investigation.
Det Supt Malyn said: “While these enquiries have been worthwhile and necessary to the investigation, they concluded without identifying a possible suspect or suspects from the DNA analysis.
“However, it demonstrates that we will continue to use forensic and other investigative work to progress this review.
“This is naturally very frustrating for the investigation team and our thoughts are very much with Claudia’s family who remain desperate for a breakthrough.
"The family have been updated about the completion of this work.
“As I have said before, the investigation will always remain open and we still receive information on a weekly basis that requires assessment and follow-up.
“People who have still yet to come forward who have visited Claudia’s house or been in her car for any reason, should still do so in the confidence that we can eliminate them against the outstanding DNA profiles.”
Call 101, or Crimestoppers anonymously on 0800 555 111.