Mr Horan said he would not treat the people of Tauranga and the Bay of Plenty so "shallowly" by running for the council, although he had been asked to stand by some members of the public.
Mr Horan ran for council in 2010 before becoming a NZ First list MP.
Mount Maunganui resident Clare Wilson, who stood for Labour in the Bay of Plenty electorate, has not ruled out standing for the seat. Mrs Wilson stood for one of the four at large seats in last year's council elections.
"I think I need to take time out and reflect how best I can support my community. I haven't really considered that fully yet, but I'm going to think carefully about if that's what I want to do next."
Wayne Moultrie, former Mount Maunganui-Papamoa ward councillor who was ousted in last year's election, said he would consider standing for the seat, depending on whether someone better qualified than he "throws their hat into the ring".
The council's other Mount Maunganui-Papamoa councillor Steve Morris said he and Mr Mitchell had worked well together as a team, both sharing similar goals for their area.
He hoped Mr Mitchell's replacement would share a concern for financial discipline and for suitable evacuation routes in the coastal suburbs.
Tauranga Mayor Stuart Crosby predicted between six and 10 people would be vying for Mr Mitchell's seat.
"Probably some of the usual suspects plus a few more. There may be people who sat for the ward or at large seats last time and possible some new comers."
Council manager of legal and governance Kirsty Downey-McGuire said if Mr Mitchell resigned on October 20 as signalled, the earliest a by-election could be held was February.
Former deputy mayor David Stewart did not want to comment.