David Crompton and the Director-General of the BBC will be asked about how the corporation came to be tipped off about a search of the singer's home.
They'll appear before a committee next month.
Yesterday Director General Tony Hall said BBC journalists "acted appropriately" in their coverage of the police raid on the singer's flat following sexual assault allegations.
The Christian is being investigated amid accusations of a incident of at a Billy Graham event at Sheffield's Bramall Lane football stadium.
Sir Cliff, who was in Portugal when the search took place, has firmly denied any wrongdoing.