But he said Thursday the decision will not be a hasty one and there were three months to consider the moral issues.
"If the information that I read suggests it's probably not wise to go and that will make a difference, then that's something I'll consider," Fleming said after leading New Zealand to an innings and 38-run victory over Sri Lanka in the second Test here.
"Like the other players I'll be reading a lot, watching the situation closely and trying to educate myself on what impact the tour will have.
"The players will take a lot of care over the decision and make sure it's the right one in their mind for the right reasons."
New Zealand Cricket (NZC) chief executive Martin Snedden has said no players would be penalised if they individually decided not to tour as a protest against President Robert Mugabe's government.
Mugabe, who has been in power since Zimbabwe's independence from Britain in 1980, won a sweeping victory in the March 31 election, but foreign critics led by the United States and the European Union dismissed the poll as a sham.
Prime Minister Helen Clark has said she is personally opposed to the tour and the leader of a minor party in the coalition government has written to the players urging them to pull out.
Fleming said he had received his letter but had not opened it yet, and said there had not been any team discussion.
"The players have to get educated, it's naive for them to make a decision without being educated.
"There's going to be a lot of material that will give them an opportunity to make a decision on whether they want to go for moral reasons.
"Safety will be discussed by NZC and that'll be their decision."
Fleming, who leaves for England on Sunday to take up his county contract as captain of Nottinghamshire, said he would talk to Zimbabwe players to help his decision.
Last year, England's tour of Zimbabwe was in doubt after Zimbabwean authorities imposed a media ban on 13 British journalists.
After a two-day delay, England's cricketers finally flew out when the ban was lifted, but cut short their itinerary.