"Unless we have some sort of setback, I certainly think that's going to happen," coach Will Muschamp said Monday.
Jones, a sophomore from Tampa, entered the offseason seemingly destined to be Florida's featured back this season. But he was hospitalized with a virus on the weekend of July 26 and spent the past month recovering from it.
He will not suit up for Saturday's season opener against Toledo.
Muschamp said Jones finally is back running, cutting and lifting weights. But he has not put on pads and practiced because doctors have feared a possible relapse.
Blood tests on Monday could be Jones' final hurdle.
Until Jones is back to full speed, redshirt junior Mack Brown will be the starter. Brown has just 40 carrries at Florida, but is more experienced than back-ups Mark Herdon, a former walk-on, and Valder Showers, a converted safety.
Behind those three sit first-year freshmen Kelvin Taylor and Adam Lane.
Whoever runs the ball the first two weeks will not be facing SEC-quality run defenses.
Toledo allowed an average of 182.3 rushing yards last season, while Miami allowed 217.9 yards a game.