The Journal had reported on Wednesday that Tesla's board members had reached out about a month ago to several executive search firms to find the company's new CEO, citing people familiar with the discussions.
Denholm said on X the report was "absolutely false" and said the EV maker's board is "highly confident" in Musk's ability to "continue executing on the exciting growth plan ahead".
Musk also said on X the report was a "deliberately false article".
Musk said last week he would cut back significantly on the time he devotes to the Trump administration and spend more time running Tesla.
Musk's work at his Department of Government Efficiency (DOGE), where he has led efforts to cut federal jobs, has been one of the most controversial aspects of the Trump presidency, and his time away from Tesla has been an additional concern for investors as sales of its ageing EV line-up have been on the decline.
His embrace of far-right politics in Europe has also led to protests against Musk and the company as well as vandalism at its showrooms and charging stations across the US and Europe.
The board members met Musk and asked him to acknowledge publicly that he would spend more time at Tesla, the WSJ report said.
But it was unclear if Musk - also a member of the board - was aware of succession planning, or if his pledge to spend more time at Tesla has affected the efforts, the report added.
Some Tesla directors, including co-founder JB Straubel, have been meeting with major investors to reassure them the company is in good hands, the WSJ said.
Activist investors have long accused Tesla's board of lacking independence and failing to rein in Musk.
Denholm, hand-picked by Musk whose controversial pay package she defended, has also drawn criticism for her own pay package along with questions about whether that compromised her oversight of Tesla and Musk.
Denholm has dismissed the allegations and a spokesperson has said her pay was fair.
In March, Denholm sold $US33.7 million in the electric vehicle maker's stock, according to a filing with the Securities and Exchange Commission.
The eight-person Tesla board, which also includes Musk's brother Kimbal Musk and James Murdoch, has been looking to add an independent director, the report said.
10°C