The 19-year-old, from Staffordshire, died on Wednesday after a four-year battle with the disease.
Stephen's appeal in aid of the Teenage Cancer Trust on his Just Giving page has now raised £3.7m.
There are now plans to make a film about his life, using footage shot over the past 12 months.
Film-maker Grigorij Richters, 26, from Hamburg, Germany, met Stephen at the Champions League final at Wembley in May 2013 and they became friends.
The visit to Wembley was on the "bucket list" of 46 ambitions Stephen wanted to achieve before he died, along with raising money for the Teenage Cancer Trust.
The pair agreed to film the bucket list together and he now has hours of footage, which he wants to use to tell Stephen's story.
Mr Richters said Stephen was "a young man who did the inconceivable, the unbelievable, at a young age".
At his former school, Chase Terrace Technology College in Burntwood, people have queued to sign a book of condolence and leave flowers.
Tributes have also been written in chalk on pavements in Birmingham.
Suggestions on social media that there should be a permanent memorial in the city will go before the Broad Street Walk of Stars committee in the summer.
Mike Olley, the manager of Broad Street in Birmingham, where the stars are located said: "We are always happy to take suggestions for the Walk of Stars.
"Many people have nominated Stephen now and I am delighted to put this before the committee."

The target waiting time for referrals is 13 weeks, but some patients must wait considerably longer.
The health and social services department tries to see patients within three months of being referred by their GP.
For some problems, such as sports injuries, diabetes or general surgery, the average wait is about six months.
Figures released by Jersey's health department show some patients referred to the hospital for bariatric surgery are having to wait over four years for treatment.
Data released by the department has shown that less than a third of specialist areas have a waiting list longer than the target.
But women needing to see a specialist before giving birth are able get an appointment right away after being referred by their GPs.
People with back pain, adult mental illness or needing breast surgery, also have less than a month to wait before they are able to see a specialist.
An appeal started by the cancer fundraiser Stephen Sutton has raised a further £400,000 - only a day after the teenager died.
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People who need to see specialists at Jersey hospital for obesity problems face an average of a four-year wait.