The 53-year-old's position as Magpies boss is believed to be under increasing pressure following Saturday's 4-0 defeat to Southampton at St Mary's.
Numerous bookmakers have installed Moyes as one of the favourites to take on the role at St James' Park, despite his failed reign as Manchester United manager.
The Scotsman lasted less than one season at Old Trafford after United fell from champions to seventh in the Premier League.
Lord Sugar wrote on Twitter this morning: "Is Alan Pardew dead man walking . Who could Mike Ashley appoint in his place . Will he de the 1st PL manager to get the sack ?
"Mike Ashley should give Moyes a chance."
Moyes has been out of work since getting sacked by United back in April.