Steve Bruce is also a popular choice among bookmakers after reports about the Magpies boss's future circulated.
The Magpies manager has been under pressure for what seems like an eternity and a promising summer transfer window at St James' Park is threatening to turn into a false dawn.
Indeed, three games into the Premier League season, Pardew's side have just two points to their name after losing to Manchester City and drawing with Aston Villa and Crystal Palace.
And bookmakers have already outlined two favourites to succeed the 53-year-old on Tyneside.
Pullis recently left Crystal Palace after reported differences with chairman Steve Parish over transfer targets.
Moyes, meanwhile, enjoyed a far from fruitful campaign at Manchester United before being sacked after less than a season at the club last term.
Another interesting selection is Hull City boss Steve Bruce, while the out-of-work trio of Gianfranco Zola, Malky Mackay and Neil Lennon are also not far behind in the running, according to the bookies.
Despite the Independent's report into Pardew's lack of job security, however, many bookmakers still think West Ham boss Sam Allardyce will be out of a job before the 53-year-old.
If Pardew doesn't want to tempt fate, though, he'll need a big result in his next Premier League clash at Southampton.
Would Pulis or Moyes be an upgrade on Pardew?