Off the record
Something said in confidence that the speaker doesn't want attributed to them.
This is an American phrase and began to be used there in the 1930s. The first citation I have of it 'on the record' is in a report of a social event attended by President Franklin Roosevelt, in the North Carolina newspaper The Daily Times-News, November 1932:
"He [Roosevelt] said that he was going to talk 'off the record', that it was mighty nice to be able to talk 'off the record' for a change and that he hoped to be able to talk 'off the record' often in the future. He told a couple of funny stones and everybody laughed and cheered."
See other phrases that were coined in the USA.