Manchester City winger Sterling supported a campaign to find a suitable stem cell donor for Damary, who had acute lymphoblastic leukaemia.
"Damary was a special young man who touched a lot of lives, including my own," Sterling said.
The England international, 24, plans to attend the funeral on Friday.
He described Damary as "an example to us all" who was "positive until the end".
The teenager's family had set up a GoFundMe page to raise £15,000 to give Damary the "best send off and celebration of life".
In March, Sterling lifted his shirt to reveal a picture of the two of them together after scoring his second goal in England's 5-0 win over the Czech Republic.
Damary's father, Tony, said Sterling's shirt tribute was "very, very touching".
"I knew they used to speak because [Sterling] came down to the hospital," he said. "They played pool together and apparently they swapped numbers."
"I remember when Crystal Palace played Manchester City and they lost - Damary put on his tracksuit with the Crystal Palace badge and took a picture to send to Raheem. They had banter with each other."
According to an appeal page, Damary did receive a stem cell match a few days before Christmas but he relapsed in February.