But he's wasting little time getting involved in the Chicago area.
On Saturday, Greene was the main attraction for a benefit with the objective of helping a family and a teacher cope with the losses they had during the recent flooding that occurred across the area.
Barrington kindergarten teacher Debbie Randall-Hayes' basement was severely damaged during April's floods. The Fox River overflowed near her Algonquin home and more than two feet of water saturated her family's basement.
"There were some heirlooms [lost]," said Randall-Hayes' husband, Brent. "All the mechanics were wiped out. The washer and dryer. The furnace. The water heater."
But it was the overwhelming amount of Randall-Hayes' teaching supplies that were destroyed that really stung.
"Over 900 books" were lost, Brent said.
When told about the situation, Greene was happy to help out, becoming the first member of the Bears' 2013 draft class to show up in the community. An event was held at Barrington United Methodist Church on Saturday. Greene signed autographs and posed for pictures. All the proceeds went to Randall-Hayes and her family.
"It was an unfortunate thing that happened to that family," Greene said. "Just to be able to help was the biggest thing. That's why I was all over it and ready to do it.
"If I have the time to do it, why not do it? It's very important to give back. Somebody always needs help somewhere. With the opportunity that I have [with the Bears], why not step up and be that person to go ahead and just help give back and help a cause?"
Greene said it's important to him to show "that you're a human being with a heart" and not just a football player. He played football with some of the children at the event and even acted like a coach. Brent said he showed his son and his son's friend how to correctly hold a football and throw it.
"He seemed to be a very personable, outgoing player," Brent said. "He was real nice. He was very laid back. He fit right in. He was easy to talk with and down to earth, good-natured."
Dealing with a flood is something Greene is very familiar with too. Last year, his mother's home in New Jersey flooded and he was there to help raise furniture and salvage other heirlooms.
"She lost a lot of her furniture. I know how damaging it can be," Greene said. "A lot of things got thrown out. It was definitely tough."
Either way, Greene said he plans on being involved in the community throughout his career. It was something he did at Rutgers, where he rose to become the Big East defensive player of the year.
"If my phone rings and I have the time to do it, I don't mind doing it," Greene said. "It's something that's great for the people for Chicago or anywhere. If I go back home in the offseason and I'm training and I get a call in Jersey or wherever I'm at training, and if there's an opportunity, I'm going to jump on it. Giving back is a main thing. To help other people is a blessing for me."
Brent said people were joking around with Greene at the event, telling him he needs to do a dance for the Barrington church after he returns his first interception for a touchdown.
"He said, 'That sounds cool. I'll be happy to do that,' " Brent said with a laugh.
The Bears would undoubtedly like that too.