Gonzalez, who will turn 23 later this month, was drafted by the Dodgers in the 27th round of the 2012 Draft, but elected instead to return to FSU for his senior season.
That did not work quite the way Gonzalez expected as he suffered a hip injury five games into the 2013 season than required season-ending surgery.
FSU petitioned the NCAA for a fifth year of eligibility for Gonzalez, which was granted.
This season, Gonzalez hit .245 and had a .410 on-base percentage for the Seminoles.
D-backs scout Luke Wren has gotten a good look at Gonzalez over the last several years.
"He can play shortstop," D-backs scouting director Montgomery said. "The bat is a little lighter, we're aware of that. We're not going to put any pressure on him to feel like he has to come out and bang the ball around the yard. I'd just be happy if he could go out and play shortstop and do the things we ask a shortstop to do."
Gonzalez was team captain in 2013 and '14 and was a three-time member of the ACC Academic Honor Roll.
The Draft concludes on Saturday, with exclusive coverage of Rounds 11-40 beginning on MLB.com at 10 a.m. MST.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. Adam Lichtenstein is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.