"Cliff has given the police evidence that he was never on his own on the days when the alleged attacks took place," an unnamed friend is quoted as telling The Sunday Times.
Sir Cliff, a devout Christian, has been questioned over allegations, including the assault of a boy under 16 at a rally for US evangelist Billy Graham in Sheffield in 1985.
The singer has never been arrested or charged, describing the allegations against him as "absurd and untrue", adding that he'd "never, in my life, assaulted anyone"
According to the Times, the friend said that detectives also found inconsistencies of an alleged victim's description of the surroundings at the Bramall Lane stadium, the location of claims made by a man who said he took part in the making of a music video with Richard in 1981.
Richard is understood to have presented evidence that he was never on his own during filming.
South Yorkshire police said: "We won't be providing a running commentary on the investigation. The inquiry continues."
On Wednesday it was revealed Sir Cliff Richard was said to be praying for the person who has accused him of committing a sex crime against a young boy.
According to friend and radio presenter Paul Gambaccini, Sir Cliff is said to have told him he was "praying to God to forgive my accuser."
Richard begins his tour in Birmingham on September 29, culminating with five nights at the Royal Albert Hall in London from October 12.
