An investigation into singer Sir Cliff Richard has "increased significantly in size" since its inception and involves "more than one allegation".
South Yorkshire's Chief Constable David Crompton said the "expanding nature" of the investigation meant he could not give a date when it would be concluded.
In a letter to Keith Vaz, chairman of the Commons Home Affairs Select Committee, Crompton said the force was in regular contact with Sir Cliff's lawyers.
The publication of the letter from Crompton, dated February 10, followed a scathing independent report into an agreement between South Yorkshire Police (SYP) and the BBC which led to a raid on the singer's home being broadcast live around the world.
The independent report found that the deal "certainly interfered with his privacy and may well have caused unnecessary distress".
Following the raid, Sir Cliff was interviewed by detectives investigating a claim of a sex crime involving a young boy, but was not arrested or charged.
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Former chief constable Andy Trotter said SYP should never have a made a deal with the broadcaster - a decision taken after BBC reporter Dan Johnson went to the force saying he knew they were investigating the veteran entertainer.
Crompton said a Metropolitan Police investigation into the source of the leak to the BBC had been unable to find the source.
In his letter, Crompton said: "South Yorkshire Police detectives are in very regular contact with Sir Cliff Richard's lawyers. Typically this involves a verbal update about once a fortnight.
"We have not written directly to Sir Cliff Richard. It is the responsibility of his lawyers to ensure he is fully briefed on the conversations which have taken place with investigators.
"This is an investigation which has increased significantly in size since its inception. Sir Cliff Richard's lawyers are aware that there is more than one allegation."
He added: "In view of the expanding nature of the investigation, it would be premature and potentially misleading to predict a likely date when it will be concluded; however, we are progressing as swiftly as possible."
Two paragraphs of the letter from Mr Crompton were blacked out before being released.