The documents suggest a press officer for South Yorkshire police was texting BBC crime correspondent Dan Johnson as the raid took place.
"Going in now, Dan," Lesley Card is allegedly to have texted.
The Christian singer lodged the papers as part of his battle for compensation from the broadcaster and the force.
Sir Cliff is claiming for damages and wants a "significant" part of his legal costs to be covered. It's believed he paid up to £1 million in lawyers' fees.
The star alleges a deal was struck between South Yorkshire Police and the broadcaster, in a writ lodged at the High Court.
A sexual abuse investigation into Sir Cliff, based on allegations from four men between 1958 and 1983, was dropped by prosecutors earlier this year due to lack of evidence. The singer always denied the claims.
The text messages, revealed by The Sun, show the reporter replied to the press officer: "Give me a shout before they take anything out, so we can get the chopper in place for a shot."
BBC director-general Tony Hall previously defended the live coverage of the operation, adding that the Commons Home Affairs Select Committee "reviewed our decisions and said we see nothing wrong in the BBC decision to run the story".
A spokesman for the corporation said: "We've said previously we are very sorry that Sir Cliff has suffered distress but we have a duty to report on matters of public interest and we stand by our journalism."
