Coulson was found guilty of phone-hacking yesterday but also faced charges of conspiring to commit misconduct in a public office by paying police officers for two directories containing phone numbers of members of the royal family.
Prosecutors are expected to announce on Monday whether he will face a retrial.
He could face up to two years in prison when he is sentenced next week over the phone-hacking conviction.
Cameron again apologised for hiring Coulson in the House of Commons today, saying he made the "wrong decision".