At least 17 people were killed as flames engulfed a block of flats in the early hours of Wednesday morning, with that death toll expected to rise in the coming days.
Sterling grew up in North-West London and began his career at Queens Park Rangers, whose ground is just a mile away from the Grenfell Tower.
"This is a deep and sad situation, one that's close to my heart and hard to swallow. I would like to help in the best way I can," he told BBC Sport.
"It is only a small step, but small steps lead to big changes if we all come together. My condolences to the affected families, also the individuals who lost their homes."
Rescue workers have said that they no longer expect to find any more survivors in the 24-storey tower block.