Newman was cut in March, but the $6 million salary-cap figure tied to his contract will not come off the books until June.
The rookie pool for the Cowboys' draft picks is $5.714 million. The team currently has about $2.14 million in cap space available.
The Cowboys have enough money to sign all their picks except Claiborne, for whom Dallas traded up to the St. Louis' Rams No. 6 overall pick in April's NFL draft, according to The Star-Telegram. The Cowboys need Newman's $6 million to work out a deal with Claiborne, who's expected to receive a contract similar to what last year's sixth overall pick, Atlanta Falcons wide receiver Julio Jones, did. Jones got a four-year, $16.2 million deal, including a $10.27 million signing bonus.
The Cowboys' financial inflexibility is one reason they haven't made a play for free-agent wide receiver Jacoby Jones, according to The Star-Telegram. Jones, who recently was cut by the Houston Texans, has a career 23.3-yard kickoff-return average with one touchdown and a career 10.2-yard punt-return average with three touchdowns.