PHOENIX -- The D-backs have retired a pair of numbers, in addition to Jackie Robinson’s No. 42.

They retired Luis Gonzalez’s No. 20 in 2010 following his retirement from baseball, and in 2015 they retired No. 51 for Randy Johnson, who had entered the National Baseball Hall of Fame earlier in the year wearing a D-backs cap.

“One is the greatest pitcher in our history, and the other is arguably the best offensive player in our history,” D-backs team president/CEO Derrick Hall said. “And they’re the most popular players that we’ve ever had wear the uniform.”

• D-backs' retired numbers

Hall is right, of course, both Gonzalez and Johnson were no-brainers to have their numbers retired. The question for the D-backs now is who’s next?

The D-backs don’t have a policy yet in place when it comes to retiring numbers, but that could soon change.

“Right now is really the perfect time to adopt one,” Hall said.

Two players jump to mind right away when it comes to who might be next: Curt Schilling and Paul Goldschmidt.

Here’s a look at each:

Schilling
This one is complicated for a variety of reasons.

Schilling was a co-MVP of the 2001 World Series, and there’s no way the D-backs would have that championship without him.

But his time with the D-backs lasted just 3 1/2 years, from July 2000 until after 2003, and after he left, the D-backs didn’t go out of their way to not issue his No. 38. It was given out a year after he departed to reliever Brandon Lyon. Luke Carlin, Sam Demel, Will Harris and Robbie Ray have also worn No. 38 since Schilling left.

Schilling’s Hall of Fame candidacy has gained steam, and it seems he has a good chance of making it next year. If that happens and he chooses to wear a D-backs cap or a cap with no logo, the D-backs could decide to retire his number.

“We would have a decision to make,” Hall said. “He’s talked about going in without a team because of his long history with the Phillies and his success here, but who knows?”

Goldschmidt
Since he was traded to the Cardinals after the 2018 season, the D-backs have not issued Goldschmidt's No. 44, and a story that Hall tells about what managing general partner Ken Kendrick told a player who wanted to wear that number gives you a pretty good indication where the club stands.

“A player had inquired about wearing No. 44,” Hall said. “And Ken told him, ‘I probably wouldn’t if I were you. Those are pretty big shoes to fill, and it’s probably a number we’re going to really consider retiring one day because he means so much to us.’”

Goldschmidt spent eight seasons with the D-backs, hitting .297/.398/.532, and he and Gonzalez rank 1-2 in franchise history in every major statistical category.

Then there’s the fact that Goldschmidt was a huge part of the Arizona community, something the D-backs take great pride in.

“[He’s] a recent player who had tremendous impact on the franchise and is a real point of pride for us as someone we drafted and developed,” Hall said. “And we absolutely love the guy.”

In the meantime, the D-backs will work on their policy for retiring numbers, walking the fine line between making sure the player is elite, but not necessarily requiring induction into the Hall of Fame.

“Obviously, we hope there’s going to be more Diamondbacks in the future in the Hall of Fame,” Hall said. “But let’s say there never are. You still want the ability to retire a uniform number of someone who has had a tremendous impact on your franchise and your community.”