Chidambaram will meet his Bangladeshi counterpart Sahara Khatun on Saturday and is expected to meet Bangladesh Prime Minister Sheikh Hasina, leader of opposition Khaleda Zia and other leaders.
The two countries had last week concluded a joint headcount in 162 enclaves on both sides of their borders. Of this, 111 are Indian territories inside Bangladesh.
The enclaves, or areas locked by territories belonging to the other side, have been an un-resolved border issue between the two countries since the partition of the subcontinent, causing untold difficulties to the people there in matters of connectivity, power and education.
Bangladesh and India share 4,096 km border of which 6.1 kilometres is still un-demarcated and a deal on this too is expected to be given finishing touches during Chidambaram's visit.
The Joint Boundary Working Group meeting between the two sides and subsequent home secretary-level talks earlier this year had decided to expedite the process of exchanging the enclaves under a 1974 Indira-Mujib agreement.Dr Singh will visit Bangladesh on September 6 and 7.