Auckland businessman Michael Barnett is likely to run for mayor in a by-election, should Len Brown resign amid the fallout from his two-year extramarital affair.

The Chamber of Commerce chief executive has put his name forward should Mr Brown, who is facing censure by fellow councillors today, step aside, RadioLive reported.

Mr Barnett, a former regional councillor, said it would be difficult but not impossible for Mr Brown to continue as mayor.

"I think he could put a group of people around him, some leaders who could help him, over the next 12 months, deliver on the promise that Auckland has bought into. I think that would be one way out,'' he told RadioLive.

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His comments come as councillors gather today to publicly censure Mr Brown.

Auckland Deputy Mayor Penny Hulse, who is chairing today's council meeting, would not say whether she would stand for mayor should there be a by-election.