The cricket chiefs of India, South Africa and Australia will get a first-hand report from Zimbabwe Cricket Union (ZCU) president Peter Chingoka at the extraordinary meeting called by International Cricket Council (ICC) boss Ehsan Mani on Thursday.
The deliberations will set the stage for a final decision on Zimbabwe at the ICC's annual conference in London on June 27, the sources said.
"The big chiefs want to hear Zimbabwe's version before they meet up with the rest in London," they said.
There was no word why the heads of the other six Test-playing nations were excluded from the Dubai meeting.
Besides the ICC chief, the other administrators at the meeting will be Jagmohan Dalmiya of India, Bob Merriman of Australia and Ray Mali of South Africa.
Zimbabwean cricket was plunged into crisis in April when 15 white players went on strike after captain Heath Streak was sacked following his demand that the selection committee be reconstituted.
The ZCU was forced to field a third-string team for two Tests and five One-dayers against Sri Lanka in May, but subsequent Test matches against world champions Australia were cancelled.
South Africa have already said they don't want to host a weakened Zimbabwe side and Cricket Australia (CA) have refused to rule out the possibility that it could press for the expulsion of Zimbabwe from Test cricket.
India, which enjoys close diplomatic relations with Zimbabwe, has declined to take sides. But it will go along with the majority at London, sources said.
There have been growing calls for Zimbabwe's expulsion from Test cricket to preserve the standards of the traditional game, while former Australian captain Steve Waugh said there was no place for teams picked on colour instead of merit.
ZCU chief executive Vincent Hogg admitted last week that Zimbabwe could be temporarily suspended from Test cricket, adding that "there could be a moratorium on Tests for six months or maybe a year."
Zimbabwe are scheduled to play Test cricket in Pakistan in October and host England in November, but both tours remain in doubt pending a final decision from the ICC.