The chairman of the Zimbabwe Cricket Union, Peter Chingoka, was among the early arrivals at the meeting but made no comment. An ICC official said a press conference was scheduled for Tuesday evening to announce their decisions.
Following British Government pressure to call off October's tour in protest at Zimbabwe President Robert Mugabe's policies, the England and Wales Cricket Board (ECB) produced a report in January saying moral concerns could form the basis for a withdrawal.
But the Government has stopped short of ordering the ECB to cancel the tour. Under ICC rules, barring a Government ban, the only other way for the ECB to withdraw without paying compensation is on security grounds.
England agreed in March last year to tour Zimbabwe in return for Zimbabwe touring England in 2003, having controversially withdrawn from a World Cup match in Harare on security grounds a month earlier.
ECB chairman David Morgan, who has been accused of going back on his word by Chingoka, faces a hard task in trying to persuade fellow ICC Board members to reverse their policy.
And if England do pull out of Zimbabwe they could consequently lose their lucrative role as hosts of September's ICC Champions Trophy One-day tournament, a mini World Cup, and the three warm-up matches with India that accompany it.
ECB chief executive Tim Lamb told Thursday's edition of the British newspaper the Daily Telegraph that being stripped of host status could mean a loss of between "four and five million pounds (seven to nine million US dollars) income we could not afford to lose."
England's Zim tour tops ICC agenda