More of New York City’s subway stations could eventually bear the names of deep-pockets sponsors — for the right price.

The Metropolitan Transportation Authority has for the first time proposed a formal set of rules for renaming its facilities, and the authority’s board is expected to discuss the proposal at meetings next week.

The authority cautioned that no name changes were imminent, and many board members have long expressed concerns about selling some of the subway system’s most significant elements to the highest bidders.

But officials said that given the authority’s perpetual quest for revenue streams, the option could not be overlooked.