Mr Conlon and the rest of the Guildford Four served 15 years of a life sentence for the attack which killed five people and injured 65, before their convictions were overturned in 1989.
SDLP MP Mark Durkan (Foyle) said Mr Conlon was promised access to the secret documents at the National Archives in Kew, west London, through the previous Victims' Commissioner for Northern Ireland, and that people could accompany him.
Mr Durkan said Mr Conlon's dying wish was that those people see the papers, which he said will not be released until 75 years after they were first circulated - 45 years longer than the standard 30 years.
During Prime Minister's Questions, Mr Durkan asked Mr Cameron: "
"Will you ensure that the dying wish of an innocent man is honoured?"
Mr Cameron replied: "I'm very happy to look at the specific request about the records at Kew which hasn't been put to me before and perhaps contact you about that issue."