After missing two months of action, Romo should be cleared from injured reserve/designated to return Wednesday and is expected to play Sunday against the Miami Dolphins, the source said.
The Cowboys won their first two games with Romo under center but have gone 0-7 in his absence, the franchise's longest losing streak since 1989.
"If we feel like, 'Just because Tony is back everything is good' -- that's the wrong approach," coach Jason Garrett said Monday. "We have to get better in all three areas. We have to coach better. We have to play better."
Garrett stopped short of saying Romo would play against the Dolphins and wouldn't declare the broken bone fully healed. But his answer could be interpreted as a green light for the 35-year-old quarterback, who has had broken ribs, two broken collarbones and three back injuries. This is Romo's 10th season as the Cowboys' starter.
"We're going to let him practice," Garrett said, noting Romo will have light work Wednesday, just as before the injury. "And if he practices well, he's going to play in the game. And we anticipate him practicing well, so we're excited about that opportunity."
"It's in the long-term best interest, if of course he's ready, to play this week," Jones said. "It's in our long-term best interest to go out there and try to win a ballgame."
Garrett also said linebacker Sean Lee passed the concussion protocol and was expected to practice Wednesday.
Cowboys reporter Todd Archer and The Associated Press contributed to this report.