Former Test halfbacks Mark Murray and Steve Mortimer believe Johnathan Thurston should be overlooked for Australia's Four Nations campaign for his own good.

With an injured Thurston struggling to keep the Cowboys captaincy, Murray felt it was in the star playmaker's "best interests" to miss Test selection.

Thurston must plead his case to North Queensland's senior management in the coming days after being arrested early on Thursday morning following a big night out.

The public nuisance charge comes at a time the two-time Dally M medal winner is racing to overcome foot surgery to make next month's Four Nations.

Thurston apologised following his drunken arrest but the Australian Rugby League is also monitoring the situation and the Test selectors are aware there's potential for sanctions.

Murray said Titans skipper Scott Prince and Melbourne Storm halfback Cooper Cronk deserved selection ahead of Thurston, who has owned Australia's No.7 jersey since 2006.

"I'd be bypassing Thurston at the moment," the former Queensland halfback told AAP.

"I think primarily his preparation physically isn't ideal but I think given the other events as well it would do him the world of good to miss a turn.

"It takes the pressure off him and lets him get organised and healthy again. The time is ideal for him to have a spell and get himself sorted."

Mortimer, who also believes Prince and Cronk should gain selection, agreed with his former 1980s Origin rival that Thurston needed to work on becoming a better role model.

"He is injured and the focus is to have 100 per cent full rehabilitation and he could do that and also he could speak to people about being a role model and lifting his game," said the Bulldogs great.

"We've got some other good halves and it may be astute for the ARL to sit him down and help address Johnathan's (issues)."

Murray labelled Cronk, the Test incumbent after Thurston missed this year's ANZAC Test win over New Zealand due to a shoulder injury, a "real pro" who is currently ensuring he's in top shape for the tournament.

"We're a bit blessed with halfbacks at the moment," he said.

"Prince would be the frontrunner ahead of Cooper Cronk.

"Either of those would do a great job. Both of them would fit into the side at either seven or 14."

But another former Kangaroos No.7, Penrith great Greg Alexander, said Thurston should remain an automatic selection if he's 100 per cent fit.

"What happened yesterday that's for the Cowboys to sort out, he shouldn't lose his Australian job because of it," Alexander said.

"But Scott Prince has had a great second half of the season with the Titans and he's ready to step in if Thurston's not fit."

Both Alexander and Mortimer also believed Roosters five-eighth Todd Carney could also slip nicely into the halfback role.

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