My theory, for what it is worth:
In the final scenes of the movie, a 'new' eye-patch wearing assassin "Gattler"working for Mr White leads the chase to recover the tournament winnings. Bond finishes him off with a nail gun shot to the eye in question, leaving the possibility that he could have survived. Noting that 'Le Chiffre' translates as 'the number', who do we know is a criminal mastermind, has one eye and is known as 'Number one'? All he is missing is the white cat.
It may be that in taking down Mr White, Bond may have promoted Le Chiffre within a sectret organisation (read SPECTRE). How long till he starts using the new psuedoname Blofeld?
I only saw this last night, so schemes still circulating... Who is to say Mr White was Le Chiffre's boss? All Mr White did was to pretend to kill Le Chiffre, thus ridding him of the attentions of the CIA and MI6. And if so, well a white 'pet' is also a little reminicent of Blofeld...