As an outfielder with the Boise Hawks, Gretzky is in town for a five-game series against the Toronto Blue Jays' Class-A short season affiliate, the Vancouver Canadians. But he is under no false illusions about what's causing the spotlight around him.
"I know it happens because of my dad," said Gretzky, whose father Wayne played 21 seasons in the National Hockey League, bringing four Stanley Cup championships to the city of Edmonton, and winning the Hart Trophy for the league's most valuable player nine times.
The baseball-playing Gretzky grew up in Los Angeles, ditching hockey at a young age to focus on football and baseball.
"If I had grown up in Canada I would've probably played hockey," he said.
As a teenager at Oaks Christian High School in California, Gretzky was named starting quarterback of the prep school's football team. Three games into his senior season, however, a shoulder injury halted his young football career.
So Gretzky turned his sights back to baseball and in 2011, he was drafted by the Chicago Cubs in the seventh round of the MLB amateur draft.
Gretzky played last season in the Arizona Rookie League, batting .304 in 25 games.
"I kind of always knew I was going to come back to baseball," he said. "I just didn't know when."
Before Boise's trip to Vancouver, Gretzky was in and out of the lineup, making appearances in just eight of the Hawks' first 25 games. Since Wednesday, he's earned three straight starts.
Hawks' manager Gary Van Tol is happy with Gretzky's performance in Vancouver so far.
"He's done everything I've asked him to," Van Tol said about Gretzky, who has gone 4-for-10 since Wednesday's game.
Through 11 games this season, Gretzky is batting .256 with 10 hits and one RBI.
"At the beginning of the year it was tough for him to find some at-bats because we do have a very strong outfield," Van Tol said. "This was an opportunity for him to really do some things and I think he's done a great job."
Van Tol, a native of Pincher Creek Alta., is well aware of the weight behind Trevor's last name. He has been impressed with the way Gretzky has carried himself.
"He's just another 20-year-old kid, really," the Hawks manager said. "He's dealt with (the media) great and he handles it very well."
As Gretzky slogs his way through baseball's ranks, he's asked to contrast his own road against the way his father was thrust into the highest levels of hockey.
"He is the Great One," Gretzky said, shrugging off the question.
Many might assume that this Gretzky made the choice to steer away from hockey to forge his own path, but the 20-year-old balks at that notion.
"Even today I never think, 'Oh I have to do something for myself.' It's selfish thinking," Gretzky said. "Everyone says it's hard to live in (my dad's) shadow, but it's really not. I respect the shadow he made, the things he's done for hockey. It's awesome."
Though Gretzky hasn't necessarily dominated his sport the way his father dominated hockey, there are similarities between father and son. Cut from the same cloth as his championship-clad father, the young Gretzky has his sights set high.
"Win a championship, that's my personal goal," he said. "You don't come here trying to get hits for yourself. That's why you played the game as a kid. You dream of being up there, getting that at-bat at the World Series and winning a championship."
His work ethic sounds like the elder Gretzky as well.
"If you play the game hard, good things will happen," he said. "That's been preached to me since I was a kid."