"Hearing more and more Barry Trotz to Washington is a done deal," Lawless tweeted.
"Capitals owner Ted Leonsis is comfortable with (Capitals President) Dick Patrick making the coaching hire. Patrick and Trotz have a long association."
Trotz spent 15 seasons as the Predators' head coach, compiling a career record of 557-479-60-100 in 1,196 regular-season games.
He, along with Lindy Ruff and Toe Blake, are the only three coaches in NHL history to win 500 games while coaching a single team.
It's unclear if the Capitals are close to hiring a new GM, though they're expected to chat with former Pittsburgh Penguins GM Ray Shero, if they haven't already done so.