Since taking over from Brad Scott, Shaw has lead the club to four wins from five matches and the players have raved about their relationship with him.
The Kangaroos made a bold play to lure Sydney premiership coach and former favourite son John Longmire back to the club, however, he turned down their offer to re-sign with the Swans for a further three seasons.
Shaw is now firming for the top job at North, but according to Barrett, the club’s contract offer would be “less than half” to what they were offering Longmire.
“The market for coaches is, when they’re in demand, they can demand the price that Alastair Clarkson and John Longmire can,” Barrett told Triple M’s The Rub on Friday.
“Rhyce Shaw is doing a really good job. Five matches ago when he took over, he wasn’t at all given a chance by that club.
“It’s a small body of work upon which they are now making decisions around him. He is now a clear favourite to become the permanent North coach.”
Jay Clark echoed Barrett’s comments, stating the support from the playing group to could go a long way in securing Shaw’s position.
“He is in the box seat to keep this North Melbourne job permanently.” Clark said on Triple M’s Dead Set Legends on Saturday.
“Most importantly here, he’s got all 44 players in his back pocket.”
“Come the end of the season, how is a coaching selection panel going to say to Jack Ziebell and 40 of his team mates ‘Nah boys I think you got this wrong’.”
“When all the players are saying ‘We love him. He’s got us playing tremendous football’.”