Rosell is believed to have met with fellow board members on Thursday and Spanish newspapers, including Mundo Deportivo and Sport, said he has decided to quit.
Barcelona have refused to comment on the reports but have announced that an emergency board meeting has been called for 6pm (1700 GMT) local time.
On Wednesday Judge Pablo Ruz issued an order to open a hearing to investigate Barcelona for the alleged misappropriation of funds over the 57.1m euro signing of Neymar and that a decision would be made at a later date whether Rosell would be called in person to give evidence.
(editing by Justin Palmer)
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