Konchar played basketball for West Chicago High School in West Chicago, Illinois. In his junior season, he averaged 19.7 points, 8.8 rebounds, 3.4 assists and two steals, leading his team in most statistical categories, as they finished with a 5–22 record. On February 27, 2014, as a senior, Konchar posted 45 points, 15 rebounds, eight assists, five steals, and five blocks in an 89–82 win over St. Charles North High School. With the performance, he became his school's all-time leading scorer, surpassing his head coach and 1983 graduate Bill Recchia. Konchar averaged 28.9 points, 14.1 rebounds, 4.1 assists, 3.2 steals, and 2.5 blocks per game in his senior season, earning All-Area MVP honors. Despite his high school success, he was lightly recruited, with his only NCAA Division I scholarship offer coming from Chicago State. Konchar attempted to join Notre Dame as a walk-on but its coaches advised him to play for nearby Indiana University – Purdue University Fort Wayne, then a joint campus of the Indiana University and Purdue University systems. On April 25, 2015, he committed to IPFW.
College career
During Konchar's college career, his basketball team represented two different universities and used three different athletic identities. In his freshman season, the school's athletic program was known as the IPFW Mastodons. Between his freshman and sophomore seasons, IPFW changed its athletic branding to Fort Wayne Mastodons. After his sophomore season, the IU and Purdue systems agreed to dissolve IPFW effective June 30, 2018. IPFW's degree programs in health sciences would transfer to the new Indiana University Fort Wayne, while all other IPFW degree programs, plus the IPFW athletic department, would become part of the new Purdue University Fort Wayne. Shortly before the split became official, the athletic department announced that it would henceforth be known as the Purdue Fort Wayne Mastodons. On March 10, 2019, Konchar recorded 18 points, 10 rebounds, and 10 assists in a 96–70 victory over South Dakota in the 2019 Summit League Tournament. It was the first triple-double in tournament history. As a senior for Purdue Fort Wayne, Konchar averaged 19.5 points, 8.6 rebounds, 5.4 assists, and two steals per game, earning first-team All-Summit League honors for his fourth consecutive season. He compiled 2,065 career points and left as the program's all-time leading scorer. At the end of the season, Tom Henry, mayor of Fort Wayne, Indiana, proclaimed March 28 as "John Konchar Day."
Professional career
After going undrafted in the 2019 NBA draft, Konchar signed a two-way contract with the Memphis Grizzlies. Konchar made his NBA debut on November 9, 2019 against the Dallas Mavericks. He suffered a calf strain on November 15 and missed several weeks. He missed a game against the Santa Cruz Warriors on January 13, 2020, with concussion protocol.