But the country has been gripped by violent protests in recent weeks, with opposition supporters insisting that Prime Minister Sheikh Hasina stand aside before elections due next month. More than 74 people have been killed since late October.
"If this situation prevails, then any big tournament or participation of any big country will be under threat," Bangladesh Cricket Board (BCB) president Nazmul Hassan told reporters late Monday.
"This must end in January and preferably in December."
The political violence has affected almost every city, including the three host venues for the T20 tournament - the capital Dhaka, Chittagong and Sylhet.
A team of International Cricket Council (ICC) inspectors declared last week they were "happy" with security arrangements but said they would continue to monitor the situation.
However, the dangers posed to teams was underlined at the weekend when a small bomb exploded outside the West Indies' Under-19 team's hotel in the port city of Chittagong, prompting them to cut short their tour.
Bangladesh is also due to host a tour by Sri Lanka in January before then staging the Asia Cup, a 50-over tournament starting in February which also features India, Pakistan and Sri Lanka.
"The quicker this political situation improves the better because the Sri Lanka tour is in January and then we have the Asia Cup. It needs to be resolved before that," said Hassan, who is a ruling party lawmaker.
In Sri Lanka, cricket authorities said they were closely monitoring developments.
"We are doing an independent security review," Sri Lanka Cricket secretary Nishantha Ranatunga told AFP. "Once we have a report, we will take a call on whether to go ahead or not.
"We are in talks with the Bangladesh board. We have to be very careful because of the every bad experience we had (in Pakistan) before." Seven Sri Lankan players and their assistant coach suffered injuries in March 2009 when a dozen gunmen opened fire on their bus in Lahore.
Sri Lanka are scheduled to play two Tests, two one-day games and two T20 matches starting January 27 in Bangladesh.
An ICC spokesman told AFP on Monday that it was "actively monitoring" the situation in Bangladesh, stressing that it gave the highest priority to the safety of all participants in ICC events.
FICA, the umbrella body for players' associations from around the cricketing world, said it was seeking advice from its independent security adviser.
"We will continue to monitor the threat levels between now and the start of the tournament and will keep players informed as to the situation," said FICA executive chairman Paul Marsh.
"As is always the case with security issues, we will ensure that the safety of our players is paramount in our decision-making. There is, however more than three months until the event starts and as such we do not need to be making any decisions at this time."
A spokesman for Cricket Australia said the board would seek its own government's advice on the security situation, but no decision on whether to go to Bangladesh would be made until much nearer the time. Australia and the West Indies both refused to play in Sri Lanka during the 1996 50-over World Cup after a bomb went off in Colombo, killing 91 people, shortly before the tournament began.