"One of those things is trade, so we are certainly going to be taking it up with the new Indian Government at the appropriate time.''
Mr Key has not met Modi in person, but said he had sent a letter of congratulations to him this week.
New Zealand began free trade talks with India in 2010 and there were originally hopes to reach an agreement by 2012.
Mr Key tried to push those along on a state visit to India in 2011 to meet Prime Minister Singh after which he said he was hopeful but there were still obstacles to get over.
Talks have stalled since then - the last round of talks were in July last year.Signing off on an agreement would help address concern New Zealand was becoming too dependent on China in its trade relations.
Fonterra has previously said India had potential to be as large as market as China.
Current two-way trade with India is at $1.1 billion and a free trade agreement was expected to more than double that to $3 billion by 2015. New Zealand's new target of trade with China is to reach $30 billion by 2020.
New Zealand is also involved in talks as part of the Asean-led Regional Comprehensive Economic Partnership (RCEP) talks launched in 2012 which include India, but is still keen to reach a bilateral agreement.