The Magpies, who will travel to the Trotters' University of Bolton Stadium for a 7pm (GMT) kick-off, reached the fifth round of the competition last year before losing to Norwich City in extra time.
The year before, they reached the last eight, only to lose an eight-goal thriller to Tottenham Hotspur at St. James' Park.
Their opponents play in the Professional Development League, a division below United, and Watson is optimistic his group can progress.
"As soon as the Youth Cup comes around, it's a massive game," Watson told nufc.co.uk. "The kids love the opportunity to perform at big stadiums and always at this time of the year, we tend to have a fully fit squad.
"All of the lads are desperate to play in the cup games so that's how highly they see it and I'm sure they'll want to give a good account of themselves."
Watson, who began his youth career at Liverpool before playing for Norwich City and Everton, will aim to ensure the occasion will not get the better of the teenagers.
He said: "They are all talking about the game and have been for a few weeks even before the draw was announced, so they are raring to go.
"There is also a case of pulling them back and making sure they don't get carried away so they can be totally focused rather than just excited and forget about what has to be done in the game.
"We've done well in the past couple of tournaments as we had some tough away trips which we got through. It was a great experience for the kids and that's what these games are for.
"There are people now in their forties and fifties but they always remember their Youth Cup games and the memory does stick with them."
Watson believes performing at Bolton's home ground will add to the occasion for his young side as well as gaining valuable experience in the early stages of their playing careers.
He added: "The lads have performed at St. James' Park before and they loved it. The bigger the stadiums then the more they can get motivated for matches.
"If you go out there and you put in a fantastic performance, it is not only a great benefit for your team, it makes other people aware of what you can do."
