Dunne won with a majority of just 701 votes in 2014 - the third smallest majority in the country - and it was suggested Labour could pull its candidate to allow Shaw a clear run at the seat.
Labour has not yet chosen a candidate for the Ohariu seat. The party's 2014 candidate, Virginia Andersen, is running in Hutt South.
Labour and Greens formally agreed in May to campaign together, and have already made an electoral agreement in the Mt Roskill by-election. The Greens did not run a candidate to give Labour candidate Michael Wood the best chance of winning.
A Labour-Greens deal could still occur in Ohariu, though there are some concerns amongst the parties that the contest may not be as close in next year's election.
The tight race in Ohariu in 2014 occurred after electorate boundary changes which might have worked against Dunne, and after a difficult term in which he stood down from his ministerial roles after being caught up in a leaking scandal.
Dunne has not had any of the same negative attention during this Parliamentary term.
It is understood the Greens are also eyeing up Nelson as a possible seat for a deal with Labour. The Greens have a solid support base in the electorate.
Such a deal would depend on whether National's Nelson MP, Nick Smith, decides to stand again in 2017.
If Smith does not run, and Labour pulls its candidate, the Greens might back their candidate - possibly a sitting MP - to cause an upset or at least build their profile against an inexperienced National candidate.