Ehsan Mani said Wednesday the situation was a worrying one though, in the light of intervention by Robert Mugabe's government, he denied it was up to him to call off the tour at this stage.
The England squad and the travelling media are due to touch down on Wednesday night in Harare for the start of a 10-day, one-day tour which has been widely condemned because of the land reform policies of president Robert Mugabe.
But on Tuesday - just 24 hours before the arrival of a strong media contingent - the Zimbabwe government released a list of journalists who would be banned from making the trip which included reporters from BBC radio and television, Daily and Sunday Telegraph, Times and Sunday Times, The Sun, Daily Mirror and News of the World.
That has prompted calls for the tour to be called off but Mani said the ICC, who had highlighted to the England and Wales Cricket Board the possible financial implications of a boycott, would endeavour to seek a resolution to the situation.
"It is of great concern. We heard about this refusal to grant visas quite late in the afternoon yesterday (Tuesday)," he said.
"I spoke to Peter Chingoka (president of Zimbabwe Cricket) and he has promised to come back to me today (Wednesday) as it was too late to speak to Zimbabwe (government) officials last night."
"I have also spoken to to the Zimbabwe High Commission."
Mani refused to accept that in the light of the media ban and the obvious political intervention by Mugabe's regime it now fell upon the ICC to call off the tour.
"That is not a matter for me to decide at this stage," he told Radio 4's Today programme.
"I believe the two matters (the tour and Zimbabwe's politics) are totally unrelated. We accept that cricket and politics do mingle but our responsibility is to cricket and it is for politicians to deal with politics. "
"Two wrongs don't make a right."
The ICC president denied there was a clause within the Future Tours Programme agreement which stated tours had to have suitable media representation.
"There is no such rule," he said. "But this is disappointing because we have been in communication with Zimbabwe Cricket for a couple of months and we had no indication until yesterday (Tuesday) afternoon that a large number of journalists would be refused entry."
When asked whether he thought Zimbabwe Cricket was in control of events, Mani replied: "Obviously not."