Ahmed Musa now plays for Turkish Super Lig club Sivasspor
Leicester, who sold the Nigeria winger in 2018, have lodged a claim for an outstanding £390,000 payment.
Al Nassr made headlines by signing Cristiano Ronaldo last year.
"The relevant bans will be lifted immediately upon the settlement of the debts being confirmed by the creditors concerned," Fifa said.
Al Nassr added Croatia star Marcelo Brozovic to their squad this summer, and have been linked with a big-money move for Chelsea's Hakim Ziyech.
-- Courtesy of BBC Sport