The conversations have so far involved companies co-owned by JPMorgan Chase, Bank of America, Citigroup, Wells Fargo and other large commercial banks, the report said, citing people familiar with the matter.
However, the newspaper said that the bank consortium discussions are in early, conceptual stages and could change.
The banks did not respond to requests for comment late on Thursday.
Stablecoins, a type of cryptocurrency designed to maintain a constant value, usually pegged to a fiat currency such as US dollar, are commonly used by crypto traders to move funds between tokens.
One bank consortium possibility that has been discussed would be a model that lets other banks use the stablecoin, in addition to the co-owners of the Clearing House and Early Warning Services, the Journal said, citing unnamed sources.