The two Otago players were not included in a list of nine players named for next month's short tour of India.
Another six players from the New Zealand A side touring India will be added to the team to play three one-day internationals, starting on October 22.
But Broom and Neesham have both missed out with coach Mike Hesson informing them of what they need to do.
In Broom's case, it is develop his game to show the skills needed to bat at No5 while Neesham needs to dominate games.
``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,'' Hesson said.
``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.''
``There are a few things that they want me to work on, wanting to bat in the middle, finishing off innings and clearing the ropes a bit more,'' he said.
It is tough for Broom but with Kane Williamson entrenched at No3 for the national side followed by Ross Taylor, the No5 spot is the vacant position in the side with all-rounders likely to occupy spots below.
He is trying to work out where he will bat with Otago. With Otago he may want to go further up the order as he will face more balls but that has to be discussed with team management.
Neesham said it was always disappointing to not be selected for a side but it would not leave a shortage of motivation to play well in the coming months.
``I won't be out to prove them wrong., just prove to them I have the ability to be in the side,'' Neesham said.
``That is just getting out there and scoring runs and taking wickets.''
Neesham said he felt his batting had really come along in the past year.
The bowling has been a bit inconsistent. It was not helped by having to come in behind the opening pair of Trent Boult and Tim Southee.
``But it is pretty simple for me. Get out there and take wickets and score runs.''
Otago starts its summer with a Plunket Shield game against Canterbury in Christchurch on October 23.
Meanwhile, legspinner Ish Sodhi enhanced his chances of being one of the six New Zealand A players to be added to the Black Caps squad with a five-wicket haul against India A in Vijayawada yesterday, NZN reports.
New Zealand A was bowled out for 147 in its first innings and the visiting side then struggled to dismiss its Indian counterpart for 320 in reply, although Sodhi played a key role in returning figures of five for 94 off 22 overs.
New Zealand A then lost Jeet Raval for 21 and Nicholls for one before George Worker (28) and Will Young (11) saw it through to 64 for two when bad light stopped play.
