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He was 74. The RJD leader is survived by his wife, three sons and two daughters.
The MP's son Sarfaraz Alam, who is an MLA, said Taslimuddin died due to breathing problem.
The RJD MP had gone to Chennai in connection with a parliamentary committee meeting. On August 24, he was admitted to the hospital after he complained of breathing problem, Alam said.
The burial may take place the day after tomorrow at his native Sisauna village in Araria district, he said.
Taslimuddin, who was a prominent Muslim leader hailing from Seemanchal area in Bihar, was an eight-time MLA and a five-time MP. He had also served as the Union Minister of State for Home.
He began his political career as a sarpanch and was elected to Bihar Assembly for the first time in 1969.
"His death has caused a void in politics," he said.
Kumar, who spoke to Alam over phone and consoled him, also announced that Taslimuddin's burial will be performed with full state honours.
The state government would bring the mortal remains of the departed leader to Patna from Chennai, the chief minister said.
RJD president Lalu Prasad and other senior party leaders Rabri Devi, former deputy CM Tejashwi Prasad Yadav, Tej Pratap Yadav, Raghuvansh Prasad Singh, Bhai Virendra and others expressed grief over Taslimuddin's death.
"Taslimuddin's death has caused an irreparable loss to the party," they said.
Lok Janshakti Party chief and Union Minister Ram Vilas Paswan said he was saddened by the demise of Taslimuddin who was known for his "frank" and "candid remarks".
JD(U) spokesperson Ajay Alok described Taslimuddin as an efficient and intrepid leader and said his death is a big loss.
RJD's Bihar unit president Ramchandra Purve said, "The party held a condolence meeting here to pay homage to the departed leader who had been a big leader of social justice movement. Taslimuddin was a big leader in Seemanchal area and it will be difficult to fill the void caused by his death.