From Crime of the Century by Michael L. Kurtz:

The press conference lasted only a few minutes during which Oswald repeated his earlier denial of an involvement in the assassination. When the conference was over, a policeman led Oswald into an elevator. A magazine photographer rode with them and talked with Oswald, who vehemently denied shooting Kennedy and asserted he was a "patsy," taking the blame for others. Just before he entered his cell, Oswald told the photographer that the truth about the assassination "conspiracy" would be revealed at his trial.

Kurtz's source was his own interview with the photographer Gerald R. Herald.

Does anyone doubt that Oswald was killed to prevent just this from happening? Columnist Jack Anderson wrote in his book Peace, War, and Politics (p. 117):

Rosselli indicated that the mob set up Oswald to take the rap. Then once the blame was placed on him, he had to be eliminated.

And (same page):

Washington cop Joe Shimon told me it was Trafficante who called on the mob's chits with Ruby and ordered him to kill Oswald.

Joe Shimon was well-connected with both the Mob and the CIA.