While training for his first-ever marathon, Will Reeve, son of the late “Superman” star Christopher Reeve, didn’t run into many problems.

He did, however, encounter a tiny dog, which sank its teeth into his ankle when he was running across a private driveway in Maine.

“A Shih Tzu nipped at my heels and drew blood,” says the 24-year-old, who works as a sports reporter for ESPN. “But I carried on running because it was just a flesh wound.

“It turned out the dog had all its shots, so now I’ve got a battle scar I wear with pride!”

Pride is just one of the motivations behind Reeve’s bid to run Sunday’s TCS New York City Marathon. The other is to personally raise $35,000 for the Christopher & Dana Reeve Foundation, the organization set up by his parents, of which he is a board member. The charity provides support for those with spinal cord injuries and raises funds for medical research.

Westchester resident Christopher became a disabled-rights activist after he was paralyzed in a horse-riding accident in 1995. Will was just shy of 3 years old at the time. Together with his wife, Dana, Christopher raised millions of dollars through the foundation, investing heavily in stem-cell research.

Tragically, almost a decade after his accident, Christopher, 52, suffered a massive heart attack and died in 2004. Just 17 months later, when Will was 13, Dana, a nonsmoker, succumbed to lung cancer at age 44.

The orphaned Reeve (who has an older half-brother, Matthew, and half-sister, Alexandra, from his father’s previous relationship with model Gae Exton) was raised by local family friends in Bedford, NY.

“Everything I do, I try to honor my parents’ legacy,” Reeve tells The Post. “I want to keep their names alive.”

Fifty people will compete under the “Team Reeve” banner on Sunday, including some of Reeve’s pals and his girlfriend.

Despite being a committed sportsman like his dad — he particularly enjoys basketball, soccer, tennis and golf — Reeve was never into long-distance running.

But he playfully admits that, for years, he would tell his family and friends at the Reeve Foundation that he would run a marathon “next year.”

“Finally I realized, ‘What kind of example am I setting when many of the people in the spinal-injury world for whom I advocate would do anything just to be able to step up to the starting line?’ ” he says.

His training started in earnest in May after phone consultations with professional running coach Mark Zenobia.

“Mark asks you every question imaginable as it pertains to your physical fitness and mental preparedness to run a marathon,” says Reeve. “I talked with him and said I wanted to do it in an acceptable time [4 hours, 15 minutes], but I [also] just wanted to finish.”

The pair devised an exercise plan, starting on Memorial Day and finishing on race day, which includes 3- to 6-mile runs during the week and a long run on Saturdays.

“I don’t run on Fridays, and the longest run I’ve done is 20 miles,” says Reeve, who lives in Soho and trains along the West Side Highway and in Central Park.

Along with almost daily runs, he lifts weights and cross-trains. “I do the occasional spin class and yoga, but mostly I’ve been focused on running, especially over the summer.”

Dietwise, Reeve says he has always eaten healthfully.

“I like to eat whole foods, whole grains and fresh meats,” says Reeve, who tends to order in from healthful places like NYC’s Dig Inn. “I’m obsessed with chicken, and could eat it three times a day.”

However, he travels frequently due to his roving reporting job for ESPN, and often has trouble finding healthy options in diners and fast-food joints. Still, he enjoys carbs once in a while at spots like Basta Pasta near Union Square.

“They have this amazing spaghetti with prosciutto that comes out of a wheel of Parmesan cheese, which they roll right up to the table,” he says. “Maybe I’ll go there for my pre-marathon loading of carbs!”

‘Everything I do, I try to honor my parents’ legacy. I want to keep their names alive.’ - Will Reeve on why he’s running in Sunday’s marathon

After the race, Reeve plans to meet his teammates before heading downtown to see friends at a bar and watch football.

“I must admit I’m looking forward to a beer or two,” he says.

So will his passion for running continue post-race? “I’ll tell you on Monday,” he says with a laugh.

Asked whether he will be thinking about his parents during Sunday’s event, Reeve replies that he will draw inspiration from their memory.

“Everything they did was the embodiment of courage, bravery and strength,” he says. “Every day was a new fight, a new battle that my parents tackled together.”

Meanwhile, he doesn’t consider his involvement in the Reeve Foundation a responsibility, but a privilege.

“My folks instilled great values in me,” he says. “One of the things they taught me from an early age is that when you’re doing something, you’d better go all the way.”