Cowboys executive vice president Stephen Jones confirmed the team has discussed cutting Carr, and his $13.8-million cap hit, as the team gets set to wade its way through free agency and the draft.
"Obviously when you're making that kind of money, you subject yourself to some discussions," Jones said, according to Jon Machota of The Dallas Morning News, "so we're obviously doing that and we'll continue to do that."
The Cowboys would save about $6.4 million this season if they let Carr go - a decision that becomes easier if the team brings back fellow corner Morris Claiborne.
"He had his best offseason and his best year," Jones said of Claiborne. "Sometimes it just takes time for young guys to really figure it out in terms of what it takes to be a pro in this league."
Jones said the Cowboys are interested in signing both Claiborne and linebacker Rolando McClain, whose agent will meet the team at the combine.
Both Carr and Claiborne have been with the team since 2012, when Carr signed a five-year, $50.1-million deal and Claiborne was drafted sixth overall. Neither recorded an interception in 2015.