"I would like to see Dhawan and Vijay open for India. Lokesh Rahul and captain Virat Kohli should come in at No.3 and 4," Gavaskar told NDTV on Wednesday.
New Zealand are touring India for three Tests and five One-Day Internationals (ODIs). The Test matches will be played in Kanpur, Kolkata and Indore.
Apart from the batting, Gavaskar also spoke about the India's bowling combination, saying that the Virat Kohli-led side should play with "three spinners and two pacers".
"The future is bright for this Indian cricet team. Apart from captain Kohli, there are ambitious players who also want to do well. The attitude and approach of this squad is fantastic," the 67-year-old former Test opener added.
The veteran of 125 Test matches, however, gave a word of caution, saying that the Black Caps should not be taken lightly.
"New Zealand spinners bundled out India in the World Twenty20. They can cause problems in Kanpur too. Their opening bowling attack can be lethal. Indian openers have to be careful," said Gavaskar.
India went down to the Kiwis by 47 runs in a group stage match of the 2016 World Twenty20 held at the VCA Stadium in Nagpur. While chasing a target of 127 runs, the home team were bowled out for a mere 79 runs in only 18.1 overs.
"New Zealand captain Kane Williamson will be the biggest threat but don't count out players like Ross Taylor and Martin Guptill. Their batting line-up is quite good too," said Gavaskar, who was the first to reach 10,000 Test runs.
The Kanpur game will be India's 500th Test match.