The 73-year-old star may be forced to miss his annual trip to the US Open Tennis if he is refused entry into the country while police investigate allegations that he sexually assaulted a young boy at an event in 1985.
An insider told The Sun newspaper: "You would be mad to try to get on a plane if you had a child abuse inquiry hanging over you."
However, people who have been questioned under caution by police can apply to the US Embassy for special consideration for a visa and will be assed on an individual basis.
The US Embassy in London said: "We do not comment on individuals."
The 'Summer Holiday' hitmaker's property in Berkshire, South East England, was searched earlier this week and items were taken away for investigation after the allegations came to light on Thursday.
Sir Cliff - who was residing at his home in Portugal at the time - has strongly denied the allegations but admits he's been aware of them for a "while."
He said previously: "For many months I have been aware of allegations against me of historic impropriety which have been circulating online.
"The allegations are completely false. Up until now I have chosen not to dignify the false allegations with a response, as it would just give them more oxygen.
"However, the police attended my apartment in Berkshire today without notice, except it would appear to the press."
The singer has not been arrested and is yet to be questioned by police.
- BANG! Showbiz