In Casino Royale, the CIA agent that offers to fund Bond after he lost the first $10M says "Once you win the money, CIA is going to get Le Chiffre." Why does CIA need to wait though? What difference does it make whether or not he lost his money?
Without the money to pay back his investors, Le Chiffre will be looking for a deal with someone else to keep him alive; almost certainly the intelligence services of a global power.
MI5 and CIA both want to bring Le Chiffre in so they can make a protection deal (against what emerges to be SPECTRE, a deal which almost certainly would have been ineffective), in exchange for the information Le Chiffre possesses about SPECTRE.