His health and a potential legal issue make that unavoidable, though.
Jones-Drew held a 15-minute news conference Monday but didn't say much about an alleged bar fight over Memorial Day weekend. Jones-Drew spoke to reporters a day before the team opens a three-day, mandatory minicamp because he "would rather get it done today than take away from what these guys are doing."
"I just don't want to be a distraction anymore," he added.
Jones-Drew declined to answer any questions or offer any details about what happened at a St. Augustine restaurant/bar last month. Jones-Drew has not been charged with any crime.
Despite a police report indicating otherwise, MJD's agent said his client was not involved in an altercation with a bouncer at the Conch House on May 26. The bouncer's attorney, meanwhile, called it an "unprovoked attack."
"Obviously, it's an ongoing investigation," Jones-Drew said. "I've been advised not to talk about it. It's an unfortunate situation. Through my career, I've tried to stay out of the media in that light -- as a distraction to this team."
Jones-Drew dodged questions about statements made by his agent and his attorney and wouldn't say whether he plans to meet with police while in town this week.
He said he was "disappointed" by all attention the incident received.
"Not only has it affected myself and the Jaguars, it affected my family as well," he said. "Frustrated? Yes. Not necessarily because of what's said in the media, but because my kids were affected by it more than anything. My children have nothing to do with what went on or what was said.
"And for children to have to deal with that was tough. That was probably the toughest thing I've had to deal with thus far. And my teammates as well. Those guys have been busting their butts and for them to have to answer questions about me is ridiculous."
Regardless, questions about the team's star running back will continue into the fall.
Even if his legal issues get resolved, his health issues will be a major concern heading into the season.
Jones-Drew had Lis franc surgery on his left foot in December, spent several months in a walking boot and was unable to fully run until recently.
He skipped the final two weeks of organized team activities so he could work out with trainers in Miami, something he has done every year since Jacksonville selected him in the second round of the 2006 draft.
He was admittedly out of shape when the team's offseason program began in April, but looked considerably more fit Monday. His most recent workout routine included full-speed cutting last Thursday, 115-pound sled work Friday and a mile run on the beach Saturday.
"Things are going on the right path," he said. "Obviously, with rehab, you're going to have some off days where it's going to be some residual pain here and there. But as long as things are going in the right direction, I feel like everything's going to be all right."
Of course, no MJD availability would be complete without him bickering with media members.
"I'll tell you one thing that upsets me," he said. "Throughout my seven years in this league, I've always played at a high level and I've trained down in South Florida the whole time; this is nothing new. I've come back in shape and I've done all these great things and yet people still question my ability to play the game. That's upsetting. That's frustrating more than what we're all here for."
Jones-Drew, who has 7,268 yards rushing, 2,559 yards receiving and 76 total touchdowns, declined to say who he was referring to.
"I read reports that I'm fat and out of shape," he said. "Yes, that does happen when you can't walk for three months and you can't work out and can't do certain things because you have to protect the integrity of your foot. But I've never put myself in a way to not be able to perform at the level I performed at since I've been here."