The Metropolitan Police have asked supermodel Kate Moss to return to Britain from the US to answer questions about allegations of drug-taking.
Assistant Commissioner Tarique Ghaffur told the Sun they wanted her to "give her side of the story".
Moss, 31, lost modelling contracts and checked into a rehabilitation clinic after pictures of her allegedly taking cocaine were published last year.
A Met Police spokeswoman confirmed that arrest was a possibility.
Mr Ghaffur told the Sun: "The investigation is progressing well and the Met is closing in on those who are behind the supply of drugs.
"But we have got to speak to Kate. I am making an appeal for Kate to come back to this country."
He added: "If she does, we will seek to see her by appointment. We will arrest her and interview her under caution."
He said there were no plans to seek her extradition from the US, where she is reportedly working and planning to live.
"I have no intention at all of sending officers to the USA or seeking her extradition," Mr Ghaffur said.
"For everybody's sake, and for her to move on, the sooner she speaks to us the better.
"We wish for the investigation to take its course, and she would be dealt with very fairly and proportionately, as would be the case with anybody else," he added.
When the scandal broke in September the UK's top police chief, Metropolitan Police Commissioner Sir Ian Blair, backed a decision to investigate the claims.
He said the possible impact of such behaviour on "impressionable young people" had led to the inquiry.
Mr Ghaffur reiterated that stance, saying: "[Sir Ian] said we would not just be taking up drugs at a street level but targeting the middle and upper classes who use cocaine."
The images were taken at a west London music studio where her then boyfriend Pete Doherty, frontman of the band Babyshambles, was recording.