Two consumer-credit giants plan to start working together to sell consumers’ data to banks, the latest attempt to feed banks’ appetite for more information on customers.

Equifax Inc. and Fair Isaac Corp., creator of the widely used FICO credit score, started pitching each other’s services earlier this month, and the companies announced the partnership Wednesday. Both companies already sell their services to banks, but now their sales employees will pitch each other’s services as well. Sometimes the companies will approach...