The young Magpies make the lengthy trip to West London to take on their Cottagers counterparts, who won the Premier League 2 Division Two title last week, at Motspur Park on Friday, 4th March (kick-off 2pm GMT).
Newcastle suffered a 6-1 home defeat against the Whites' second-string last week but Turner-Cooke, who has netted nine goal in his previous 11 games at under-23 level, is hopeful his side can avenge their heavy loss upon their trip to the capital.
The 18-year-old, who joined the Magpies' youth set-up from Sunderland in January 2021, told nufc.co.uk: "We played Fulham last week and they are a very good team. It'll be a tough test. We'll work hard in training, have a game plan that we'll stick to and hopefully we'll give them a good game.
"We're very determined. It was an embarrassing result and none of us want to feel like that again in any game. It's a quick turnaround and we're going down to try and win the game.
"Every game we play in, we want to win. We're in the final of the (Northumberland) Senior Cup and we want to get as far as we can in the Premier League Cup. We'll be going down to Fulham hoping to get through to the next round."
Newcastle's youngsters head into the cup contest off the back of a thrilling 4-3 away win at Norwich City on Monday night, recovering from 3-1 down to stage a late comeback against the Canaries.
Turner-Cooke, who scored a brace in the Premier League 2 encounter, was delighted to contribute towards an important victory in Norfolk, maintaining Newcastle's hopes of qualifying for the Division Two play-off spots in the process.
The teenager added: "As an attacking player, I want to score as many goals as I can. Thankfully, I got another two goals and an assist so I want to continue my goalscoring season and get another good amount of goals before the end of the season to help the team get promoted.
"We knew we needed a big performance against a good side in Norwich on Monday.
"We conceded a few sloppy goals that we need to cut out but to go away from home against a team currently second in the table, score four goals and come away with a win was massive.
"It has made the team more determined to get promoted this season. It's one of the best ways to win in coming from behind, especially away from home.
"The character and determination in the squad is really good and now we need to go and build on from it."
