The Magpies face four of last season's top six in their opening five fixtures, with Tottenham Hotspur coming to St. James' Park in the first match before home games against Chelsea and Arsenal either side of a trip to champions Manchester City.
Rafa Benítez's men also face a long trip to South Wales to face newly-promoted Cardiff in their second match and former Newcastle favourite Anderson admits that it could be a "tough" first few weeks for United.
But the ex-Republic of Ireland international, who made more than 300 United appearances between 1982 and 1992, insists his old club don't need to fear anybody - particularly on home soil.
"It could been kinder, that's for sure," Anderson told nufc.co.uk. "Tottenham, Chelsea, Manchester City, Arsenal and Manchester United in there as well - it's a tough start.
"But you've got to remember we beat Manchester United here (last season), we beat Arsenal and we beat Chelsea.
"On paper, it looks a tough start, it looks a little bit daunting, but you've got to play them at some stage of the season - and I think you're better getting them out of the way early, to be quite honest.
"The opening day of the season, Spurs at home, is an attractive fixture and the second game's not a bad one either - Cardiff, newly-promoted.
"There's four top sides in those opening five games and when you get some of the top sides early in the season, it can be a good thing.
"If we look back to the Tottenham game last season, even though we lost, I didn't think Tottenham were great; I thought we could have got something out of the game, and I think sometimes you're better off playing these top sides early when they haven't got into their stride.
"They're still finding their feet and you've got to remember that a lot of these boys from the top sides are coming back from a World Cup as well.
"Hopefully we can take advantage if they're a little bit on the tired side. They'll get an extra week, maybe ten days off from their clubs, so will they be as sharp as they normally would be? Hopefully not, and hopefully we'll be able to take advantage of that."
Looking beyond the opening ten games, Anderson - now a summariser for BBC Newcastle - believes the festive period could be an interesting one for the Magpies.
"Liverpool away on Boxing Day is a big one and then on New Year's Day, Manchester United at home," he said.
"I think everybody looks at those holiday fixtures, and they're big ones for us. I don't think you can get a bigger game than Liverpool away on Boxing Day, and most definitely Manchester United at home on New Year's Day, you couldn't ask for much bigger than that.
"They're two that really catch the eye, the ones that really jump out and hit you."
See Newcastle United's full 2018/19 fixture list here.
