New Zealand was the first developed country to sign a FTA with China and has been pushing for an upgrade after other countries including Australia signed FTAs on more favourable terms in some areas. A focus will be on eliminating non-tariff barriers (NTBs).
And Trade Minister Todd McClay has said he wants New Zealand to play "a very big role" in China's new Silk Road strategy, known as One Belt One Road, that aims to invest trillions of dollars in overseas infrastructure projects.
The South China Sea dispute could also be discussed during Li's visit.
Li made an unusually detailed defense of China's build-up of military equipment on artificial islands in the sea during a press conference in Australia, where he travelled to New Zealand from, saying it was to maintain "the freedom of navigation and overflight in the South China Sea".
Another delicate issue could be the Ministry of Business, Innovation and Employment's anti-dumping investigation into Chinese steel - launched despite the Chinese Government saying the allegations were a "wild guess" with "no merit".
Li, named by Forbes Magazine as the world's 12th most powerful person, heads China's government and executive and manages the implementation of national economic development policy and the state budget.
That focus on the economy has seen him develop a relationship with English, who as Deputy Prime Minister hosted Li's 2009 visit to New Zealand. English has also met with Li while in Beijing, and the two were involved in discussions on the Asian Infrastructure Investment Bank.
New Zealand agreed to become a founding member of the bank in 2015, established by China as a counter-weight to the World Bank and International Monetary Fund.