Staveley was instrumental in brokering the deal that allowed Saudi Arabia's Public Investment Fund to buy 80 percent of Newcastle in October 2021.
Along with her husband Ghodoussi, Staveley initially held a 10 percent stake in Newcastle.
Both Staveley and Ghodoussi were heavily involved in running Newcastle after the Saudi-backed takeover and oversaw the appointment of Eddie Howe as manager in November 2021.
Newcastle finished fourth in the Premier League in 2022-23 to qualify for the Champions League and also reached the League Cup final.
They fared less well last season, crashing out of the Champions League in the group stage and finishing a disappointing seventh in the Premier League.
Staveley and Ghodoussi's shareholding was diluted to six percent due to recent equity raisings which the pair have not participated in.
The BBC reported on Wednesday that the pair are due to leave the club, but Newcastle are yet to comment.
The £300 million ($385 million) Saudi takeover from previous Newcastle owner Mike Ashley attracted huge attention, in large part because of controversy over the Gulf state's human rights record.
Staveley helped push the deal through after it stalled before finally concluding in October 2021 when the Premier League received assurances there would be no Saudi state involvement.
