But that was under one stipulation. He wanted his son to talk first.
"It's his big day," Orel said.
Being selected Wednesday afternoon is a lot more about the 23-year-old's journey as a ballplayer than simply being the son of a Dodgers great.
"It's something I've dealt with my whole life growing up," Jordan said. "I feel like once I got past the high school ranks and into college, I kind of knew what I can do for myself. I kind of look forward to the pressure."
Bearing the Hershiser surname was only one of the obstacles the fifth-year senior from USC had to overcome. And that was the easy part.
The hard obstacles came in the form of two arm surgeries.
The first came after his freshman season at USC, when he was overworked playing summer ball and needed Tommy John surgery on his right elbow. His father still takes the blame for that one.
"I think the biggest disappointment as a dad was I protected his arm until he was a college freshman," said Orel, who added Jordan's summer-ball coaches allowed him to throw more than 100 pitches in a game for the first time.
"There is so much to be learned for any parent to continue to watch out for their child and their health."
After missing all of 2009 and all but three games in '10, Hershiser was back and healthy. That is until a shoulder surgery ended his '11 season after only two appearances.
The young pitcher rehabbed again and returned to the mound in 2012, appearing in five games and allowing one earned run in 5 1/3 innings pitched in relief.
"It's a long time coming being a fifth-year senior going through two arm surgeries," Jordan said. "So it's a good stamp on the rehab process and getting back to where I needed to be."
He continued working out at USC and 1,046 picks into the Draft, Jordan got a call from the Dodgers, telling him that the team he grew up watching his dad play for wanted to give him a shot.
For Jordan, the pick came as a surprise. He didn't want to get his hopes up and be let down after all he went through.
"I was trying to expect not to be drafted to brace for the worst," he said.
Jordan's dad even started exposing him to business opportunities if that happened, impressing his family outside off the baseball field as much as he has on it.
"Most of the people I'm introducing him to are hoping that baseball doesn't work out so that they can hire him," the former 1988 World Series MVP said with a laugh.
But they will have to wait as Jordan continues to give baseball a shot. Despite not being pressured by his dad to pick up the sport along with the difficulty of living up to his accomplishments, Jordan has played baseball most of his life. There was one point when Jordan gave up the game to play golf, and his dad hired a coach who helped him lower his handicap below five.
However, Jordan gravitated to baseball, and he started pitching again once high school rolled around.
"He was making his own choices, but he definitely saw there were issues growing up with the name," said Orel, who added he faced his own pressures coming up and not having any sort of athletic lineage. "He wasn't going to back down from them, but he was going to make his own choices of where he wanted to land."
With an upbringing centered around baseball, Jordan had many opportunities other boys weren't given. He spent afternoons growing up in the Dodger Stadium locker room talking to Tommy Lasorda and his dad's teammates. Like a sponge, he would try to absorb as much knowledge as he could.
If he was curious, he could just turn to his father.
"He would be a dad first," Jordan said. "But if I asked him enough questions, he would turn into a pitching coach, for sure."
For Orel, he just wanted to be there for his son.
"People are more impressed with the fact that he doesn't wear the Hershiser name on his sleeve with all the things he got to do," he said.
Now, Jordan is excited about playing for the team his dad once helped lead to a World Series title. He can't help but imagine being back in the same locker room he got to visit as a kid. He said he's dealt with the pressure his whole life and he just wants to go out and prove that he's good enough to be the son of a former 204-game winner.
"I like being back in Dodger blue," he said. "I'm really just looking forward to getting started."
As for whether there are any Cy Young Awards in his own future, Jordan just laughed at the thought.
"I'm just trying to go get innings in Rookie Ball right now," he said.
Alex Angert is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.