As part of a caucus reshuffle, Mr Goff would lose the Auckland portfolio to avoid confusion about what role he was fulfilling when he attended Auckland-related events.
Mr Little said the MP would cover any of the costs of his mayoral bid, and this would not come out of his Parliamentary expenses. That included travel and mobile phone costs.
Christchurch Mayor Lianne Dalziel resigned as a Labour MP ahead of her mayoral campaign in 2013.
Mr Little said it was up to MPs to decide when they stood down.
"[Mr Goff] has said he will step aside and take leave from Parliament during the formal period of the campaign, that four to six-week period. I think that's the right thing to do."
If Mr Goff wins the mayoralty it would spark a by-election in the Mt Roskill seat he has held for three decades.
Mr Little said he did not expect to run as a candidate in the electorate.