As US regulators home in on at least three banks in a probe of manipulation of a key benchmark rate, investigators face challenges proving wrongdoing because banks report and obtain borrowing costs in an opaque process that leaves a scant evidence trail, according to people familiar with the situation.

Even if the case does identify manipulation, it could present regulators with the larger challenge of either preventing further abuses of the London interbank offered rate, which currently is tied to $10 trillion in loans and $350 trillion in interest-rate derivatives, or finding an alternative.