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Whiter, 24, was helping his friend change a tyre when he was struck by another car near Newmarket in Suffolk.
Jan Adamec, 40, admitted two counts of causing injury by dangerous driving and will be sentenced in September.
"People have been in touch from the Paralympic side, I'd love to get involved," Whiter told BBC Look East.
"I can only dream and hope that one day I could be there. If I can focus with sport, it is going to help me progress more within myself and get me through these times."
Whiter's friend and Soham Town Rangers player, Joey Abbs, suffered serious leg injuries in the incident.
Although he expressed an interest in disability sport, Whiter did not specify which sport he would attempt.
Speaking at a fundraising event for his rehabilitation in Exning, Suffolk, Whiter said: "You've got to have a dream, you've got to start somewhere.
"I know how hard it is to win a medal at the Paralympics, I'm not saying I am going to turn up and do it, but I would love to go."
Former Newmarket Town footballer Shaun Whiter hopes to reach the Tokyo 2020 Paralympics after losing both his legs in a hit-and-run incident.