The 54-year-old McClaren, who was manager of Newcastle's north east rivals Middlesbrough from 2001-06 before taking over as England boss, is expected to be confirmed in the role later on Wednesday, according to local media.
Should McClaren take over, he faces a major rebuilding job at a club that narrowly avoided relegation from the Premier League after a dreadful second half of the season.
Carver was handed the reins at the turn of the year following Alan Pardew's move to Crystal Palace, but the team won only three games under his stewardship.
Despite keeping Newcastle in the top flight, Carver's long association with the club ended on Wednesday.
"After discussions with John it was mutually agreed that in the best interests of the club moving forward, and to enable the new head coach to build his own coaching team, we would go our separate ways," managing director Lee Charnley said in a statement.
"He is a man of great character and dignity and will always be welcome at Newcastle United. We wish him every success in the future," he added.
"It has been a privilege to serve as head coach of this great football club," Carver said.
"The fans and the region deserve a successful team and both myself and my support staff worked very hard with the squad that was available to us."
Stone, a former England international, had been a coach at the club since 2010.
(Reporting by Amlan Chakraborty in New Delhi; editing by Sudipto Ganguly)
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