The former England boss won just six of 28 Premier League games in charge of the Magpies, who are just one place off the foot of the table.
McClaren and his team were booed off following Saturday’s 3-1 loss to Bournemouth at St James’ Park – their third successive league defeat.
Former Liverpool, Chelsea, Real Madrid and Inter Milan boss Rafael Benitez has been tipped to take over.
McClaren’s future has been a source of almost constant speculation since the defeat to the Cherries.
Match of the Day presenter Gary Lineker tweeted: “Newcastle have finally put Steve McClaren out of his misery.
“The running of that great football club is beyond shambolic.”
Ian Dennis, BBC Radio 5 live’s senior football reporter, said Benitez had been identified as a replacement for McClaren at a board meeting on Monday.
“Rafa in the driving seat to replace McClaren,” tweeted former Magpies striker Michael Owen. “Whoever takes over, I still expect Newcastle to stay up.”
McClaren, 54, signed a three-year contract with the Magpies in June after the club avoided relegation on the final day of last season.
Newcastle’s next game is at leaders Leicester City on Monday.