In addition to the physicals, there are contract details that need to be worked out before the trade could be completed. Barron has yet to sign his restricted free-agent tender offer of $2.62 million. Carpenter, in the last year of his contract, has an incentive clause worth up to $1.895 million that the Rams might want to renegotiate.
On Thursday, ESPNDallas.com reported that the teams were negotiating the swap of first-round picks who failed to live up to expectations.
Carpenter has been unable to earn a starting job with the Cowboys since being drafted in 2006. The Cowboys picked up his potential replacement in Penn State linebacker Sean Lee in the second round last month.
Barron, a first-rounder in 2005, was called for an NFL-high five holding penalties last year and has allowed 33 sacks in his career.