WASHINGTON—The Office of the Comptroller of the Currency has granted preliminary conditional approval to a closely watched charter application from World Liberty Financial, moving the Trump family-tied cryptocurrency venture closer to operating a federally regulated national trust bank.

The OCC said World Liberty Trust Company, N.A., would be headquartered in Bay Harbor Islands, Fla., and operate as a wholly owned subsidiary of WLTC Holdings LLC.

The proposed bank would issue and redeem…