In her column Ms Collins credited Orakei Local Board member and centre-right politician Mark Thomas with courage for declaring he was standing for the mayoralty but said he did not have a huge profile - "which really is needed to win".
"Auckland's mayoralty needs guts, determination, intelligence and presence. Who's up for it?" she wrote.
The centre-right has struggled to find a high profile mayoral candidate since John Banks lost to Mr Brown at the first Super City elections in 2010.
At the 2013 elections, the little known businessman John Palino carried the centre-right banner. He polled 108,928 votes to Mr Brown's 164,338.
Stephen Berry, the right-wing candidate who came third in 2013 with 13,650 votes, has announced he is standing again next year.
Labour MP Phil Goff is expected to announce next month that he is standing for the mayoralty.
Mr Brown, whose second term has been marred by an affair with a council adviser, has not said if he will be seeking a third term.
Another confirmed candidate is activist Penny Bright, who is fighting the council over $33,372 in unpaid rates on her Kingsland property.
She has refused to pay rates since 2007 until she knows where her money is going.