Michael Vaughan's team face Zimbabwe in the third of four one-dayers here on Saturday with the final match taking place on Sunday before they make a hasty retreat to South Africa.
But before they make their eager departure, Mani is determined to sit down with the squad and hear what they have to say.
" want to see them because it is very important to hear their views," said Mani.
"I want to know what they think about the level of cricket in Zimbabwe and their experiences in the country so far."
Mani, whose organisation had the power to fine or even suspend England if they had refused to pull out of the trip, insisted he appreciated the players' worries over being dragged into a political war of words over the Robert Mugabe regime.
Vaughan had insisted his players would withdraw from the tour if it became politicised.
"I felt it was important for me to be here because there have been concerns about this tour and I wanted to see it for myself," Mani told reporters.
The ICC chief also said that England's reputation in world cricket has been enhanced by their decision to go-ahead with the tour and that David Morgan, the chairman of the England and Wales Cricket Board (ECB), should be praised for his work.
"I could see that England were caught between a rock and a hard place, but he (Morgan) has been absolutely superb, honest and totally up front with people," said Mani.
"He has had to deal with a lot of domestic pressures, which is understandable because of the unique situation between England and Zimbabwe. The issue was not going to die down."
England are confident of pulling off a clean sweep of the four-match tour after convincing wins in the first two games with wicket-keeper Geraint Jones looking to the weekend's back-to-back games to enhance his reputation.
Jones, who took over from Chris Read in the summer, has already made a Test century but has looked far from the finished article in the one-day set-up.
However, he hit 66 off 46 balls during a record sixth-wicket partnership of 120 with Kevin Pietersen in the second match on Wednesday, to help set England on their way to victory.
It was was his first one-day half-century.
"I haven't been given the situation to go out and show what I can do with a good wicket and plenty of time to bat," said Jones.
"I was mindful of the fact that it was a great situation to go out and score some runs and also put the team in a good situation to go 2-0 up in the series."