The 6-foot-6, 237-pound senior simply shrugs it off.
"I'm not really worried about that," Jones said. "That's something that, if it happens, it happens. If we keep winning things like that will take care of itself.
"That's something that I never think about or even worry about."
But a handful of unofficial Heisman projections have, mentioning Jones' name as a candidate for the most prestigious individual prize in college football. The latest came Monday when a story in The Memphis Commercial Appeal said the senior should be a serious candidate and called him "perhaps the most electric college QB since (former Virginia Tech and current Atlanta Falcons Michael) Vick."
Of course, Jones must churn out big numbers and guide the Razorbacks to big wins during a brutal stretch this month to be considered. The Hogs get another chance to play in front of a national audience Saturday when they meet No. 16 Florida in Ben Hill Griffin Stadium in Gainesville, Fla., in a game televised by CBS.
But Arkansas coach Houston Nutt said Jones deserves the recognition now.
"I'm partial, but I've been saying that for a long time," Nutt said. "I think Matt does belong in the Heisman conversations. Again, he always talks about team and puts team first. But I just look around at other people and names that get mentioned and I know what they do for their teams and I know what Matt does for our team.
"He's been doing it for the last four years. He's a true difference maker."
Jones is off to an impressive start, leading Arkansas to a 3-1 mark by throwing for 838 yards and 6 touchdowns and rushing for 245 yards and 2 more scores. He is first in the SEC in total offense (270.8 a game), second in passing yards a game (209.5) and third in passing efficiency (160.5 rating).
In addition, Jones is the SEC's 10th-leading rusher (61.2 yards a game).
Jones' 60 yards Saturday helped him inch closer toward the Southeastern Conference's all-time rushing record for quarterbacks, a mark he should set in October. He is 123 yards shy of passing former Mississippi State quarterback John Bond (2,280), who has held the record since 1983.
Jones broke former quarterback Clint Stoerner's school record for touchdown responsibility against the Crimson Tide when he ran for a 6-yard score in the first quarter. He also threw a touchdown pass to running back Peyton Hillis and has accounted for 64 scores in his career (44 passing, 20 rushing).
"I don't know how all that works, (Heisman Trophy) conversations or whatever," Jones said. "It would be awesome, but it's not one of my goals I have. I don't really set a lot of individual goals as far as 'I want to win the Heisman. I want to win this, I want to win that.'"
Arkansas tailback Cedric Cobbs was mentioned in early-season Heisman talk in 2003 when he rushed for 562 yards and 5 touchdowns during Arkansas' 4-0 start. But the senior's name disappeared when he was injured against Florida and never resurfaced after the Hogs lost three straight games.
Nutt doesn't think the attention will be detrimental to the Hogs if it happens again.
He said last season's experiences -- when five juniors left early for the NFL Draft and several seniors pondered their futures -- served as an important lesson.
"I think there was a learning curve right there where they understand that good things happen when your team wins," Nutt said. "You get more recognition, more eyes are on the team. That's the way I feel. I think they can handle it much better."
Arkansas hasn't beaten Florida since 1982, when it knocked off the Gators 28-24 in the Bluebonnet Bowl. But the Hogs remember how close they got last season, trimming a 26-point deficit to 33-28 in the fourth quarter.
"They dominated the whole game until the fourth quarter," said defensive end Jeb Huckeba. "You could really feel the momentum changing. It was an emotional roller coaster. We felt like we had a chance and then we didn't."
Arkansas' rally ended when free safety Tony Bua was flagged for a personal foul penalty after a late hit on Florida quarterback Chris Leak. Linebacker Sam Olajubutu intercepted Leak's pass on the play, but the penalty gave Florida a first down that helped them hold on for the victory.
"He was really down," Huckeba said of Bua, who is now playing for the Miami Dolphins. "You can't blame one person. Sometimes the ref is going to make that call and sometimes he's not. He's a guy who played really hard for us so it wasn't like we were really disappointed in him because of the plays he made before."
Hillis' two touchdowns Saturday pushed him atop the SEC in scoring. The Conway native has six touchdowns in four games and Nutt said the freshman is "so strong-willed and has a great nose for the goal line." ... Arkansas' offense led the SEC in several statistical categories last week. But after the Alabama win, the Hogs only hold the top spot in scoring offense (39.8 points a game). ... College Football Wire, which emphasizes wins against quality opponents, moved Arkansas up 22 spots to No. 23 in its poll this week. Florida isn't ranked in College Football Wire's top 25.
Jones Included In Heisman talk
Hawgs Daily Top Stories
Cats Picked To Win SEC CrownThe voters at SEC Media Days are convinced: Kentucky has reloaded.
AllWildcatsWednesday at 10:13 AM
Arkansas On Game Days | Tailgate TravelsAs much fun as it is being at an Arkansas football game, the pregame can be just as enjoyable, especially if you have an RV. Head out to Fayetteville to see what makes the…
Scout CFBFriday at 9:20 AM
"They Are Playing Really Good Football"Arkansas Coaches Bret Bielema and Dan Enos talk about facing Auburn this weekend and the challenges that presents for the Razorbacks.
Inside The AU TigersWednesday at 9:26 AM
Scout's Top 25 Recruiting ClassesScout has a new top school in the recruiting rankings. Take a look at capsules for the top 25 classes in the country, including a new number one.
Scout 2017 Rankings DirectoryThe Scout positional, state, regional, national and team rankings for the Class of 2017...