But instead of developing an ego, Chicago's top prospect is taking a humble approach to Minor League life.
Even though he is most comfortable in center field, the 21-year-old, at the direction of the White Sox, has been more than willing to spend part of his offseason in Arizona, refining his skills in the corner outfield spots.
Thompson, one of seven Chicago prospects playing for the Salt River Rafters in the Arizona Fall League, just hopes it means a faster ascent to the Major Leagues.
"Heck, if they want me to play catcher, I'll do it," Thompson joked. "They told me to come here and play all three outfield positions, and I've done that so far. It's a big adjustment because I'm happy in center field, but if they want you in left, you'll play in left. You can't say no. Whatever they ask, I'm going to do."
Thompson, who is the son of former Lakers and Trail Blazers star Mychal and brother to current NBA players Klay and Mychal Jr., just finished a season he started at Advanced-A Winston before making stops late in the year at Double-A Birmingham and Triple-A Charlotte.
The 2009 second-round Draft pick combined to hit 25 homers in 2012 while batting .253 and boasting a .328 on-base percentage.
"It was a good year, I expected a little more out of myself in the first half and I came around a little bit in the second half," Thompson said. "It was a successful year, though. I learned a lot. There were peaks and valleys, but the end result, ending up in Triple-A and getting some playoff experience, I enjoyed that."
Even though he had already played in 136 games before heading to Arizona, Thompson still doesn't feel tired, comparing the experience to when he was growing up and participating in multiple sports throughout the year.
"This is baseball, it's fun," Thompson said. "It's a long season, but that's what I signed up for. I'm used to it. When I was a kid, I was always playing either baseball, basketball or football. It's just like that. I always work hard to hopefully play 160 or 180 games each season."
In his 34 at-bats in the Fall League, however, Thompson has struggled to collect hits, totaling just six so far. He has shown patience at the plate, though, amassing 11 walks.
Because he isn't playing every day, and his usual rhythm is hard to maintain, the outfielder isn't worried about the numbers he puts up, just as long as he is stringing together quality at-bats. Cutting down on the 166 strikeouts he recorded in 2012 is also a goal.
"I could line out four times in a game and I'd be happy," Thompson said. "I'm just trying to be as productive as possible. I can only help myself out here no matter what I do."
White Sox hitters in the Fall League
Carlos Sanchez followed the same path as Thompson, beginning in Advanced-A and finishing the year at Triple-A. Ranked No. 7 on the White Sox Top 20 Prospects list, Sanchez hit .323 overall in 2012 with 25 doubles and 26 steals. In 57 at-bats in the Fall League so far, the 20-year-old third baseman has 15 hits (.263), 12 RBIs and eight walks.
Andy Wilkins played in 116 games for Birmingham this season, batting just .239. He did, however, hit 17 home runs and 28 doubles while driving in 69 runs. The 24-year-old first baseman's power and patience earned him 63 walks this year, giving him a .335 on-base percentage. The Arkansas product has dominated Arizona pitching in his first 66 at-bats, collecting 20 hits (.303).
White Sox pitchers in the Fall League
Andre Rienzo is ranked as the No. 18 prospect in the White Sox organization, and turned in a 2012 campaign to prove it. Throwing 103 1/3 innings between Winston, Birmingham and Charlotte, the 24-year-old boasted a 2.53 ERA, while striking out 113 batters in just 18 starts.
Rienzo is in Arizona to make up for lost time because of a 50-game suspension earlier this year for testing positive for performance-enhancing drugs. In four Fall League starts so far, Rienzo has kept up his torrid pace, giving up just five earned runs in 16 2/3 innings.
Santos Rodriguez appeared in 42 games between Birmingham and Charlotte as a reliever, finishing with a combined 2.90 ERA and 69 strikeouts. The 24-year-old has struggled in his first eight appearances in Arizona, surrendering five runs (four earned) on seven hits.
Salvador Sanchez is one of the oldest players in the Fall League at 27. The New York native only threw 30 1/3 innings this season and is trying to get more work under his belt. He has only allowed two earned runs on four hits in seven appearances so far in Arizona.
Taylor Thompson was drafted twice by the White Sox before finally signing out of Auburn in 2009. The right-handed reliever threw 44 1/3 innings for Winston in 2012 while striking out 57 batters. He has given up 11 hits in just 8 1/3 innings in the Fall League so far, but has only allowed three runs.
Tyler Emerick is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.