All were, however, excited to be in a contest with Labour Napier spokesman and former List MP Stuart Nash - the only nominee for his party's candidacy, expected to be announced on Monday.
Mr Nash said all three "looked like worthy candidates".
"Whoever ends up running, I look forward to it being a good, clean campaign," Mr Nash said.
"Whoever gets the nomination, I will ring them up, we'll have a cup of coffee. I don't think it will be a campaign where there's any animosity."
Mr Goodfellow said he was "extremely impressed" with the "talent" that had come forward to contest the Napier selection.
"Chris Tremain will leave big shoes to fill in this seat, but the calibre of candidates I've seen today gives me great confidence National will field a very competitive candidate for this year's election," he said.
Electorate head Lynne Trafford said: "This is an exciting time for the National Party in Napier. This process gives party members the opportunity to participate in a highly democratic process which ensures candidates are selected by their own communities.
"This is one of the fundamental reasons why party membership is so important, and such a great opportunity to pursue an interest in politics at any level."
The prospective candidates will address and answer questions from local delegates at four formal "meet the candidate" meetings over the next three weeks.