Scully, who is the fifth minister to hold the gambling brief since the review was launched, was asked when the white paper was to be published on the BBC's Politics Live programme.
He replied: "All I can say is it's in the next few weeks, I really want to get it out of the door."
The minister said he had been in a meeting with gambling reform campaigners including Gambling With Lives before the programme, adding: "I want to make sure I get it absolutely right rather than rush it."
However, when pressed whether "in the next few weeks" meant the white paper would be published before Christmas, Scully answered: "It depends how you define that."