But Schilling, ever the realist, doesn't see it happening in 2014, his second time on the ballot. And for that matter, he's skeptical it will happen in 2015, either.
There are two pitchers on the 2014 ballot this season that Schilling views as shoe-ins: Greg Maddux and Tom Glavine.
And next season, two of the aces Schilling had the privilege to share a rotation with, Randy Johnson and Pedro Martinez, will be eligible. John Smoltz is also on his first ballot in 2015.
"I don't think I have a shot this year," Schilling said in a recent interview with MLB.com. "If I remember right, just about all the pitchers are first-ballot guys this year and next year. This year and next year, you have Maddux, RJ, Glavine, Pedro and Smoltz. And they are all first-ballot guys."
The results will be announced exclusively on MLB Network and simulcast on MLB.com live on Wednesday at 2 p.m. ET as part of a three-hour live show beginning at noon. On Thursday, MLB.com and MLB Network will air the news conferences featuring the electees live from New York at 11 a.m. ET.
Schilling's regular-season numbers -- 216-146, 3.46 ERA and 3,116 strikeouts -- make him a bubble candidate for the Hall.
However, throw in what he did in October and it isn't hard to imagine Schilling one day in the middle of an induction ceremony in Cooperstown, N.Y. In 19 postseason starts, Schilling went 11-2 with a 2.23 ERA.
The righty pitched in the World Series four times (1993, 2001, 2004 and 2007) and for three different teams (the Phillies, Diamondbacks and Red Sox).
Three out of those four teams won it all, while the '93 Phillies were sent home on that walk-off homer by Toronto's Joe Carter.
"You know what, the fact that I was considered on that many ballots is cool," said Schilling. "Whether I believe [I belong] or what I think is irrelevant. I know what I did. At the end of the day, when I think about my career, the thing I always tell people that I wanted when I started was, I wanted to have a career where the 24 guys I suited up with, if their life depended on a win or a loss, who would they want to have the ball? I wanted to be that guy."
Schilling is 15th on baseball's all-time strikeouts list. Of the 14 men in front of him, the only ones who aren't Hall of Famers are Johnson, Roger Clemens, Maddux and Martinez.
Though Schilling fancies himself as a baseball historian, he said that his Hall of Fame candidacy isn't something that keeps him up at night.
"I played with Randy Johnson," said Schilling. "And Pedro wasn't at his best when I played with him, but he should be a unanimous choice. I played with a hobbling Dale Murphy. The guy was the most dominating player in the '80s for a while. I don't understand how he's not in the Hall. If it doesn't work out, I can look at some guys who don't have plaques and say, 'Wow, I'm all right.'"
Whether or not Schilling winds up in Cooperstown, he had a career filled with indelible moments.
Who could forget Game 6 of the 2004 American League Championship Series against the Yankees, when Schilling had a loose ankle tendon sewn back into place so he could pitch? With blood leaking through to his sock, he won that game, keeping the Red Sox alive in their quest to become the first team in history to recover from an 0-3 deficit in a postseason series.
"We literally were the most focused I'd ever been as a team, or I'd ever seen anyone as a team for that period of time," Schilling said. "And that's why we won."
Schilling went through the painful procedure again before Game 2 of the '04 World Series, and silenced a heavy-hitting Cardinals team. The Red Sox swept, winning their first World Series since 1918.
In 2001, he teamed with Johnson to dethrone the Yankees, who had won the World Series the three previous seasons.
"October gave you something you didn't have, from an adrenaline perspective. But I think there was a sense of accountability and responsibility I wanted," Schilling said. "I wanted everything to matter on me. I wanted that ... There's a couple of statistics or things I walked away from that I remember. And I know stats. I know my stats. I believe the number is five.
"I pitched in five win-or-go-home games. My team was 5-0 in those. I never lost a game that would end my team's season. Every game I took the ball, we won those games. I loved that."
Though Schilling's heroics for Philadelphia in '93 are overshadowed by what he did for Arizona and Boston, that's where his postseason lore started.
"I remember my first postseason game against Atlanta in '93. We weren't supposed to beat them," Schilling said. "Maddux and Smoltz and Glavine and [Steve] Avery. [Terry] Pendleton, [Ron] Gant. We were the scruffy dudes from Philly. And I went out there and struck out the first five hitters of the game. In five hitters, the entire momentum of the Series, I thought, changed. I realized what I was capable of doing by myself on the mound. I realized -- that's powerful."
While some players have fuzzy memories of their accomplishments, Schilling remembers everything down to the smallest detail.
"In the '93 World Series, we're down [in games], 3-1," Schilling said. "[The Blue Jays] scored 15 runs the night before; this offense had the top three hitters in the American League -- [John] Olerud, [Roberto] Alomar and [Paul] Molitor -- and we win [Game 5], 2-0. I learned in those games that, as a starting pitcher, it's just like being a quarterback. I can change everything based on my actions."
His peak, Schilling remembers clearly, was 2001.
"I still believe that the '01 postseason, those were the best 48 innings I ever threw," Schilling said. "I threw 305 innings that year, and my best 48 were at the end."
Not only craving the October spotlight, but thriving in it, is something that separated Schilling from a lot of others.
"I've talked to guys, great players, unbelievable players, Hall of Fame players who were teammates, who were terrified of October," Schilling said. "They viewed that as a way to screw up everything you did during the season. I was like, 'Wow, what a loser mentality that is.' You realize in life, that's exactly how life is. Fear is a motivator or a paralyzer -- it's one of the two. I was always motivated by it."