David Cameron has said he will "look at" the possibility of fulfilling Gerry Conlon's dying wish.
Mr Conlon and the rest of the Guildford Four served 15 years of a life sentence after being wrongly convicted of the IRA's 1974 Guildford pub bombing.
Five people were killed and 65 injured.
The convictions were overturned in 1989.
SDLP MP Mark Durkan told the House of Commons that Mr Conlon had been promised access to secret documents relating to the bombing at the National Archives in Kew, west London, by the previous Victims' Commissioner for Northern Ireland.
Mr Durkan said Mr Conlon's dying wish was that people see the papers, which he said will not be released until 75 years after they were first circulated.
He asked the prime minister: "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."