The investigation into Sir Cliff Richard has "increased significantly in size" and involves "more than one allegation", police say.
South Yorkshire's Chief Constable David Crompton said the "expanding nature" of the probe into an historical sex offence 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, Mr Crompton said the force was in regular contact with Sir Cliff's lawyers.
The publication of the letter from Chief Const 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 British 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.
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.
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