Speaking to Jonathan Ross in front of advertisers, ITV's director of television admitted that the gameshow's first series suffered "a bumpy ride".
Fincham is quoted by The Guardian as saying: "It is a big show, the sort of thing ITV should be doing on a Saturday night. [It's a show I] want to make some changes to… I'm nearly there, but not quite ready yet."
After Ross asked him whether a second series was certain, Fincham said: "I haven't made that decision yet."
Meanwhile, a Red or Black source admitted that ITV might have financial concerns about the format, which cost £15m to make.
"The feeling is it might come back as a big Saturday night show but it's a question of how you work that logistically and make it work if it's just once a week - it's a big expensive show," the insider speculated.
Despite mediocre viewing figures, ITV's chief executive Adam Crozier maintained last month that the programme "really caught the imagination", delivering "a fantastically young and valuable advertising audience".
Red or Black was embroiled in controversy after its first £1 million jackpot winner Nathan Hageman turned out to be a former convicted criminal.
Watch footage of ITV1's Red or Black below:
> Frank Skinner: 'Red or Black was a glimpse of hell'