The two players have been heavily linked with the St George Illawarra Dragons for months, with multiple publications reporting previously that the club were in discussions with the two young forwards before picking up Luciano Leilua.
Luki has a player option for the 2025 season but could opt for a move away from Townsville and sign on with a new club from the cessation of next season.
Per SMH, he also toured the facilities at the St George Illawarra Dragons in Wollongong in December last year.
"Yes, we are confident," Reibel said of keeping the pair via AAP.
"We are still talking to the management of Heilum and Kulikefu. They are both fine young men and both good on and off the field with what they do.
"They have bought firmly into our system in North Queensland and want to be part of that.
"We will continue talking to their management and make sure we get the best outcome."
The 22-year-old Luki is consistently rated as one of the best young players in the game but has yet to reach his full potential after being hampered by injuries and selection issues in Townsville, who have had an abundance of second-rowers across his career.
Despite that, he has managed 38 NRL appearances, scoring ten tries and impressing when given the opportunity to perform on the field.
The Dragons are also interested in teenage sensation Kulikefu Finefeuiaki, who is able to discuss his future with interested rivals as he is yet to confirm his future beyond the 2024 season.
Already widely regarded as one of the best young edge forwards in the game, the 19-year-old made his debut at the Cowboys in the middle of the 2023 season and was upgraded from a development contract to a full-time contract in April.
His 12 games coming between Round 10 and the end of the season saw the second-rower become an important part of Todd Payten's side, although his spot isn't guaranteed moving forward.
It has been understood in the past that The Dolphins have also shown an interest in Finefeuiaki, and a move from the club would allow him to remain in Queensland.
It's reported that those clubs potentially in pursuit are talking of a figure at around $600,000 per year, which will be a tough pill to swallow on the Cowboys' salary cap if they do fight to keep the 19-year-old.
Both Luki and Finefuiaki will be on full-show this weekend for the Cowboys as they take on The Dolphins at at Suncorp Stadium on Sunday afternoon.