A judge in London said a statement containing the information should be provided by a senior Metropolitan force officer relating to the Operation Yewtree inquiry.
Sir Cliff is suing the BBC, and South Yorkshire Police, over reports naming him as a suspected sex offender.
He launched legal action in the wake of coverage of a raid at his apartment in Sunningdale, Berkshire, in August 2014.
The singer has been described in written submissions by his lawyers as having suffered ''profound and long-lasting'' damage.
The BBC has said it will "vigorously" defend the action.
At a preliminary hearing on Monday, Mr Justice Mann said the BBC's application related to proceedings brought by Sir Cliff, the "well known entertainer", against it and the Chief Constable of South Yorkshire Police arising out of the raid.
He said Sir Cliff had "formally asked" the BBC whether its source for the story was within Operation Yewtree, which was conducted by the Met.
The judge added: "The BBC seeks to resist disclosing information on the ground that it would, or could, compromise its source."
Mr Justice Mann said: "In order to make its case, the BBC seeks to ascertain the number of people within Yewtree who might have known about the investigation at the time in order to be able to, as I understand it, put flesh on the bones of what would otherwise be a vague assertion as to the risk of identifying the source if the pool is small."
He pointed out: "The BBC decline to make any admissions at all whether the source was within Operation Yewtree.
"The BBC seeks to get information as to the size of the pool from the Metropolitan Police."
The judge said the application was made in relation to a further hearing next month which will deal with the "important" issue of protection of sources.
That hearing will centre on whether or not the BBC should be required to answer the question whether its reporter's source was "to the best of his knowledge or belief" from within Operation Yewtree, or a person who had obtained the information from a member of the team.
Sir Cliff's lawyers say they are not asking for information which might reveal the source's identity.
Mr Justice Mann has previously been told that in late 2013, a man had made an allegation to the Metropolitan Police, saying he had been sexually assaulted by Sir Cliff at a public event at Sheffield United's Bramall Lane football stadium in Sheffield as a child in 1985.
Metropolitan Police officers had passed the allegation to South Yorkshire Police in July 2014.
Sir Cliff had denied the allegation ''as soon as it was brought to his attention'' and in June last year, prosecutors announced he would face no charges.
The singer says his privacy was invaded and he wants "'very substantial" damages.