At least that's what the Steelers' actions are telling us.
Last week, the Steelers placed the low tender on Cockrell. That means the Steelers could lose the restricted free agent to another team for a fourth-round draft pick, if the Steelers don't match the offer.
And beginning today at noon, the Steelers, according to a team source, will begin negotiating with veteran free-agent cornerbacks in the hope of replacing -- or at least bringing in someone to compete with -- Cockrell for his starting job.
Both of those starting cornerbacks are capable of starting and playing more press coverage for the Steelers, but neither will be 28 years old by opening day and would likely cost more than the Steelers are willing to pay.
If that turns out to be the case, the Steelers would keep Cockrell and make drafting a cornerback out of this year's rich draft crop a bigger priority.
The Steelers can begin negotiating with league free agents today at noon but can't sign anyone until 4 p.m. Thursday.
The Steelers enter free agency approximately $21 million under the salary cap, following the new contracts for Antonio Brown and James Harrison, the $12.1 million franchise tag on Le'Veon Bell, and the $1.8 million tenders for RFAs Cockrell and Chris Hubbard.
It's the biggest cushion the Steelers have enjoyed entering free agency, but they're also planning extensions for Stephon Tuitt and Alejandro Villanueva (costing approximately $5 million in this year's cap money) and need $2 million for their rookie class, $1.2 million for their practice squad and another $1 million when the cap expands to include 53 players. The Steelers would also like to enter the season with an emergency fund for injuries of about $4 million.
All of that leaves the Steelers with about $8 million in free-agent spending money, which could buy a pair of mid-tier players, such as Ladarius Green and Mike Mitchell, who respectively carried first-year cap hits of $2.4 million and $2.2 million upon signing with the team.
That would leave room for potentially re-signing Lawrence Timmons, but the Steelers say he wants more money than they're willing to pay.
The Steelers also believe they'll lose WR Markus Wheaton to another team in free agency.
Along with Timmons and Wheaton, Steelers free agents who can begin negotiating with other teams today at noon are: David Johnson, Jarvis Jones, Landry Jones, Ricardo Matthews, Shamarko Thomas, Cody Wallace and DeAngelo Williams.