The Cowboys are waiting for former cornerback Terence Newman's contract to expire on June 1 before signing any of their seven rookie draft picks.
Newman was cut in March, but the $6-million cap figure tied to his contract will not come off the books until June.
That means first-round pick Morris Claiborne will remain unsigned until next month.
The rookie pool for the team's draft picks is $5.714 million. Dallas currently has about $2.14 million in salary cap space available.
Report: Claiborne Can't Sign With Cowboys Until June