A win over the New York Giants on Sunday would place Brady in more elite company. He would join Hall of Famers Terry Bradshaw and Joe Montana as the only quarterbacks to lead their team to four Super Bowl titles.
As football fans and followers debate where Brady stands in NFL history, there are some in the baseball world who still wonder what might have been had the Patriots star made a different career choice.
Long before becoming a football icon, Brady was a promising left-handed-hitting catcher out of Junipero Serra High School in San Mateo, Calif.
"He was a legitimate prospect," said Gary Hughes, a longtime scout who was hired by the Red Sox on Thursday. "I guess he made the right decision, obviously. I knew he was a football player; I didn't know he was that kind of football player. I had no idea he was that good."
Brady was from a tradition-rich high school baseball program, which also produced standouts like Barry Bonds and Gregg Jefferies.
Hughes, who worked with the Marlins in the 1990s, scouted Brady in high school.
"Obviously he had very good size," Hughes said. "When you see guys that big, there are only a few guys you can compare him to. He was obviously athletic and had a very good arm."
In the 1995 First-Year Player Draft, the Montreal Expos selected Brady in the 18th round. Then a 6-foot-4, 200-pounder, he was the 507th overall selection.
If not for a football scholarship at the University of Michigan, Brady may have been taken as high as the fifth round, according to Jim Fleming, the Miami Marlins' special assistant to the president of baseball operations.
In 1995, Fleming was a West Coast crosschecker with the Expos' scouting department.
"I'd say five, six, seven -- around there," Fleming said in reference to what rounds Brady may have been selected in baseball if not for his football option. "We said if he got into the teens, we'd take a shot. We weren't going to spend a pick [in the first 10 rounds] on him, because there was so much uncertainty on him."
As a prospect, Brady was viewed as a big, tall catcher with some bat speed. He had power potential and a strong throwing arm.
"He [was drafted] in the teens because he was going to Michigan to play football," Fleming said. "We took him down a little lower and worked with him over the course of the summer. I think we got him to consider baseball, but in the end, his heart was in football."
History has proven Brady made a wise career choice. But his road to stardom didn't come easy. At Michigan, he initially struggled for playing time because the Wolverines also had a quarterback named Drew Henson.
Like Brady, Henson was a talented baseball player -- so much so that he was a third-round pick of the Yankees in 1998, and he played briefly for New York in 2002 and '03 before going back to football, where he spent time in the NFL with the Dallas Cowboys, Minnesota Vikings and Detroit Lions.
When Brady was at Michigan, the Expos kept tabs on him in case football didn't pan out.
"[When] he wasn't playing, we thought he may go back to playing baseball and give it another shot," Fleming said. "He never did."
Entering the 2000 NFL Draft, teams weren't completely sold on Brady either. He was a sixth-round pick and the 199th overall choice.
Twelve years and five trips to the Super Bowl later, it's obvious the Patriots made the right choice -- and so did the big high school catcher.
Joe Frisaro is a reporter for MLB.com. He writes a blog, called The Fish Pond. Follow him on Twitter @JoeFrisaro. MLB.com reporter Chris Haft contributed to this report. This story was not subject to the approval of Major League Baseball or its clubs.