Both players were in New Zealand’s squad for the Champions Trophy in England earlier this year and failed to set the seen alight as the Kiwis failed to reach the knockout stages.
Broom has been told to develop his skills as a number five batsman in the 50-over format as the number three and four positions in the order will be occupied by captain Kane Williamson and senior player Ross Taylor.
Neesham, who scored 47 runs at 23 and took no wickets at the Champions Trophy, will have to show more consistency with bat and ball in domestic cricket if he wants to fight his way back into the side.
Black Caps coach Mike Hesson said: “It will be disappointing for James and Neil, but we’ve talked through the areas that we’d like to see them work on and if we see development, they’ll certainly both come into the reckoning come the home summer.
“Neil was really effective for us batting at three or four last season, but we have quality, established batsmen in those positions and we’d like to see Neil develop his game further to show he has the skills to bat at five.
“Jimmy needs go back and really dominate domestic cricket with both bat and ball. We know Jimmy is a talented player, but we’ve spoken with him around improving the consistency in all areas of his game.”
New Zealand have only selected nine players in the initial squad with six to be added from the New Zealand A team that is currently touring India.
Hesson said it is a great incentive for the A team players to fight for selection in the senior national side.
The Kiwi mentor said: “With a number of our top guys already playing in India, it’s helpful to be able to select the squad in two parts.
“With six spots left, there’s an obvious incentive for the players in New Zealand A to perform and put their best foot forward.”
The first of the three ODIs will take place in Mumbai on 22 October while the teams will also contest three T20Is in the first week on November.
NZ’s initial ODI squad for India: Kane Williamson (captain), Trent Boult, Colin de Grandhomme, Martin Guptill, Tom Latham, Adam Milne, Mitchell Santner, Tim Southee, Ross Taylor.