The grainy images in the Daily Mirror tabloid prompted several fashion houses to sever ties with the 31-year-old, although her career has begun to recover since she left a drug rehabilitation clinic in the United States in October.
"We would like to appeal for her to return, see us, and tell us her side of the story," said London police Assistant Commissioner Tarique Ghaffur.
"For everybody's sake, and for her to move on, the sooner she speaks to us the better," he said in a statement on Thursday, adding that the mother-of-one would be dealt with "fairly and proportionately as would be the case with anybody else."
He said the net was closing in on other suspects in the case and that arrests were likely. A police spokeswoman added that none had been made so far.
Police do not intend to seek Moss' extradition from the United States, where media reports say she is planning to settle permanently with her three-year-old daughter Lila Grace.
"What we have done so far is conducted searches of the studios where the matter was filmed, in addition to obtaining the full digital recording of the incident which is currently being closely studied by the investigative team," Ghaffur added.
The pictures were taken in a London studio where Moss' then boyfriend, rock singer and self-confessed drug addict Pete Doherty, was recording. British newspapers have reported the couple has now split up.
POLICE TARGET "UPPER CLASS" USERS
The scandal in September prompted British fashion house Burberry and Swedish-based Hennes and Mauritz to cut ties with one of the most famous faces in fashion. France's Chanel also said they would not renew a contract with Moss when it expired.
Some fashion insiders criticized the labels, arguing that the use of illegal drugs like cocaine was already known to be widespread in the industry.
British police have made a point of targeting not only street dealers and users, but also what it calls "middle class and upper class drug users."
Moss, whose gaunt features ushered in the "heroin chic" fashion style of the 1990s, never confirmed cocaine allegations made against her, but issued a short statement after the scandal broke, apologizing to people she said she had let down.
Her London lawyers and modeling agency could not immediately be reached for comment on Thursday."
LOL, This story is a joke. While there at it why don't they ask osama bin laden to come to America and turn himself into police?
