The Daily Mail says Graham, who recently scored his first goal for the Black Cats, has given Gateshead's JJ O'Donnell £2,690 after he was struck down with sesamoiditis, an injury to the foot.
That causes O'Donnell's toes to inflame, making kicking a ball excruciating.
Two Gateshead supporters launched an online campaign this week to fund the operation - hoping to generate £5,000.
And Graham chipped in with over half of that on Monday, writing on the fundraising page: "Good Luck!! Hope the operation is a success."