The young Magpies, who received a bye to the last-eight stage, make the short trip to Hillheads Park (kick-off 7.30pm GMT) to face the Northern League Division One outfit, who compete in the ninth tier of English football.
Ndiweni, who signed his first professional contract with his boyhood club last summer, admitted the squad are relishing the quarter-final tie against senior opposition and is expecting an unorthodox test against the Seahorses.
The 18-year-old striker, who hails from Throckley, told nufc.co.uk: "Everyone is excited and looking forward to the game. We're in the quarter-finals and, ultimately, we want to try and win a trophy at the end of the season.
"It'll be much different to a Premier League 2 or Premier League Cup game. It'll be more direct, physical and we have to find a way around it to beat them. Whether it is through 90 minutes or penalties, we just want to get through to the semi-finals.
"As professional players, it's important that we behave professionally and treat this game as any other, trying to do a professional job on the day because they will be good. We can't underestimate them and they will be a challenge.
"We know how teams in this division play like. We played Ashington and North Shields in the cup last season, winning both on penalties, so they did take us far in those matches and both had quality."
Newcastle's second-string reached the final of last season's competition before suffering a narrow 3-2 defeat against National League North side Blyth Spartans at St. James' Park.
Ndiweni, who scored 14 goals in 17 appearances at under-18 level last term, is keen to use last year's misfortunes as an incentive for the current campaign.
The teenage forward, who joined Newcastle's youth set-up in 2016, added: "It was disappointing last season not to come away with the win against Blyth in the final so we want to make things right this year.
"It's good motivation for the team as we were in that losing position and we don't want to experience that again so we'll do everything we can to be on the other side of that and winning the cup.
"To win the competition, especially after what happened last season, would be great and it's always nice to have a piece of silverware at the end of the season."
Tickets for Wednesday's Northumberland Senior Cup quarter-final, taking place at Hillheads Park, are priced at £7 for adults and £5 concessions.