Sri Lanka this week reiterated their offer to step in at short notice should the ICC deem Bangladesh unsafe for both the T20 and the Asia Cup late next month.
"We have the grounds and the necessary infrastructure to host an event like that at short notice," Sri Lankan Cricket secretary Nishantha Ranatunga said.
If it lost the hosting rights it would be a serious blow to Bangladesh.
There were warning signs on New Zealand's tour there in October that all was not well.
If the ICC decides to drop Bangladesh it would not be without precedent.
In 2008 it postponed the Champions Trophy, scheduled for Pakistan, soon after a bomb at Islamabad's Marriott Hotel killed 55 people.
The tournament was then staged in South Africa the following year.
New Zealand Cricket Players' Association boss Heath Mills has some worries over the safety of players given the domestic situation, post election.
"It's fair to say we do have concerns about the security situation," he said yesterday.
"There has been a stepping up of violence and protest in the wake of the election."
Mills said there was a need to know the security plans were sufficient "but more importantly are they capable of delivering on those plans"?
International players federation boss Ian Smith and NZC's security consultant Reg Dickason are among those who will attend the meeting. Bangladesh are due to host the 16-team tournament from March 16 to April 6, which also involves a 10-team women's tournament.