The petition was launched at the end of last week by Nick's family following the news a 75-year-old Lincoln man is receiving the drug for free for at least three months, funded by the Lincolnshire Teaching Primary Care Trust (TPCT).
The drug, called Sutent, is not available free on the NHS and Nick's family and friends have been paying the £4,200 a month by fund raising.
Nick's mother Sandi, manager of New Look fashion store, Skegness, said: "We were declined on the grounds the drug was experimental which it isn't because if it was, why are they giving it to this man?
"It does work. If the PCT took the trouble to talk to us they would see that.
"This has been going on for six months. Originally they told me if we could pay for three months and prove it was working they would help us. But now they're denying it."
Nick, 24, was diagnosed with kidney cancer last November and was given just six weeks to live.
More than 50 forms have gone out into the community showing how much Nick's plight has captured the hearts of the town.
Sandi plans to present the petition personally to the PCT.
The family has tried everything to get the drug funded and at the moment everything they do is aimed at raising money.
They are even on a 'baked beans' diet to save money.
Sandi said: "Nick has said he never sees us because we are always fund raising.
"If we get funding we can concentrate on him which is really what it's all about."
Copies of the petition are available at New Look, Lumley Road, the Standard office at The Hildreds, and at many local businesses in the town.