Doctors have told Wilson, in no uncertain terms, that he faces an increased risk of a neck injury if he plays again, sources familiar with the situation told ESPN.
The same sources said that at least one doctor whom Wilson recently met with is leaving the decision in the running back's hands.
Wilson, who was placed on season-ending injured reserve Thursday, wants to continue playing and expects to return next season, a source told ESPN.
Wilson suffered the neck injury in Week 5 against the Philadelphia Eagles.
The Giants said earlier this week that further tests on Wilson's neck had shown improvement in his herniated disk, but that he was not yet cleared to resume football activities.
The Giants' first-round pick in the 2012 draft, Wilson was in line for a significant role as the starting running back this season. But he fumbled twice in the season-opening loss at Dallas and was benched later in September.
ESPN.com Giants reporter Dan Graziano contributed to this report.