Mashrafe and Rasel had been doubtful for the tournament after picking up injuries two weeks ago but both have made good progress, chief selector Faruk Ahmed told.
''We have got a positive report from the team physio on Rasel.
Hopefully he will be okay before our first match against Sri Lanka on Oct 7 at Mohali,'' he said.
The pair will also play against West Indies and Zimbabwe in their remaining two qualifying games. Two teams will qualify for the main event, which takes place between Oct 15 and Nov 5.
''We don't like to target any particular opponents. Rather we will be looking to win all three qualifying games,'' coach Dav Whatmore said.
Bangladesh, due to leave for India Oct 1, will play a warm-up match against a Punjab team at Chandigarh on Oct 5.