The source said Jones wants to evaluate the injury and to weigh options concerning what the team should do with him with respect to his injury-list status.
Jones, a third-year wideout, hasn't played in a game this season and has participated in only five practices since the start of training camp because of a series of lower-leg-related injuries.
Expected to be the No. 2 receiver to A.J. Green, Jones was slowed in camp because of an ankle injury that the source confirmed goes back to February. Once the injury healed two weeks later, Jones returned for only three practices before he broke his left foot.
Jones has since practiced only once during the Week 4 bye and one other time prior to the Week 5 game against New England, during which the Bengals said he "tweaked" an ankle.
The source said the belief is that Jones broke his other foot trying to overcompensate for the injury to his right ankle. The source also said doctors didn't know what any of the problems with the ankle were until just after the "tweak" when he saw a specialist.
NFL.com reported late Sunday night that surgery was being discussed internally as a possible course of action.
When asked Monday if he saw Jones' injury progressing, coach Marvin Lewis said, "No."
Jones was the Bengals' second-leading receiver behind Green last season with 51 receptions for 712 yards and 10 touchdowns.
The Bengals could again be without both receivers this week as Green (toe) told ESPN's Bob Holtzman on Sunday that he would not play against Indianapolis.