Mani also revealed that ICC chief executive Malcolm Speed had flown to Harare for talks with the Zimbabwe Cricket Union (ZCU).
When asked by reporters at Lord's in London on Monday if suspending Zimbabwe was an option, he replied: "No. Zimbabwe are a full member of the ICC and they will be treated the same way as any other member."
Zimbabwe's team has been rocked by the axing of 15 white players, many of them senior cricketers, including former captain Heath Streak, admist claims that the Zimbabwe Cricket Union is operating a quota-based selection policy.
Mani, speaking at the launch of the ICC's Champions Trophy One-day tournament due to take place in England in September, said the world governing body had been monitoring the situation in Zimbabwe.
"There's been a lot going on behind the scenes. We've been in very close and intense dialogue with the ZCU," Mani said.
"We are concerned about the integrity of Test cricket," the Pakistani insisted.
"They (the ZCU) are having a board meeting later today (Monday) and Malcolm is meeting with them tomorrow (Tuesday). There may be some developments we can report then."
A severely weakened Zimbabwe side is now taking on Sri Lanka in a home Test series.
They lost the first match by an innings and 240 runs and look like going down to a similarly huge defeat in the ongoing second Test in Bulawayo.