Jones, who did not play last week and is out this week, needs the procedure to repair damage done to his meniscus during the preseason. The source said Jones-Drew does not have ligament damage, the newspaper reported.
The Jaguars said Friday that Jones-Drew would not play in the season finale against the Houston Texans.
Rashad Jennings will start as the injury-depleted Jaguars try to win the AFC South title on the last day of the regular season. The Jags have to win and the Colts must lose to the Titans in order for that to happen. If both the Jags and Colts win, Indianapolis wins the division on a tiebreaker.
"They told him going into this year that knee may not hold up," said Jaguars offensive coordinator Dirk Koetter, according to the Times-Union. "It's really pretty remarkable that he put up the numbers that he did and ran the way he did for as long he did."