"He's certainly very close to playing," Sri Lanka coach Graham Ford said on Wednesday. "He was probably going to play against South Africa and then the game got reduced and there was the chance he would've been bowling with a wet ball.
"He was going to get a game there and he's certainly not here just to carry the drinks."
Ford said the 18-year-old Dananjaya, who bowls four varieties of spin, could be a useful weapon.
"He's got a lot of variations with good control and it's going to take any batsman who hasn't seen him a bit of time to work out what he does," said Ford. "In this format of the game that's quite an advantage."
Mendis strained his side a week ago in the group match against Zimbabwe. MRI scans showed he had a slight tear in his left side.
New Zealand captain Ross Taylor expects spin to play a part in the Super Eights as all matches will be double-headers.
"Spin has been very successful in this form of the game," said Taylor. "With two games tomorrow, the wicket could deteriorate and take a bit of turn for the second game and not the first game.
"The main message is to be aggressive and not let them settle."