The pair fought a controversial draw in Los Angeles in December, with many people believing 30-year-old Fury had won, despite being knocked down twice, BBC Sport reported.
American Wilder, 33, said, "I think 100 percent it's going to be done, it's just a matter of time.
"It's not if it happens, it's when it happens and we are looking at late April or early May."
The original fight was scored 115-111 for Wilder, 114-112 for Fury and 113-113, with Fury's second knockdown in the 12th-round proving crucial.
The draw was the first time either man had not been victorious in a professional fight, after Wilder had won his first 40 contests and Fury had won his previous 27 bouts.
For Fury it was his first title matchup since he beat Wladimir Klitschko for the IBF, IBO, WBA and WBO belts in 2015 before he was out of boxing for more than two years.
"A lot of people doubted Fury because of the outside things going on in his life but he had six months of training, he showed up and gave a great performance," added Wilder.
"It was so controversial and everywhere I go it's all that people are talking about and they want to see a rematch. I can't see myself drawing with anyone – there has to be a winner. This is what people want and I'm so excited.
"His team are all scared and they do not want him to fight but Tyson Fury is a man of his word."
Wilder, who said a rematch with Fury would take place either in Las Vegas or the Barclays Center in New York, was asked about the chances of fighting Anthony Joshua, who holds the IBO, WBA, WBF and WBO titles.
"Everyone has to fight everyone," said Wilder. "We have to move on with my career and they (Joshua's promoters) tried to slow it down as they felt they were the man of the division and everything ran around them."