Carroll said Sunday after Okung, the replacement for retired All-Pro left tackle Walter Jones, missed another workout that the deal already should be done given that the No. 5 and No. 7 picks have signed.
Carroll said missing the first days of camp works "immeasurably against" the rookie.
The coach, who also has executive vice president powers in personnel with the Seahawks, said the team is ready to get the contract done right away. He added "it's pretty clear how this should work: They have to pick up the phone."
The Seahawks signed their other first-round draft pick, safety Earl Thomas to a five-year, $21.1 million contract Saturday. Thomas, the 14th overall pick, received $12.31 million in guarantees.
The Associated Press contributed to this report.