"The resolution will be brought at 11 a.m. on January 27," state Parliamentary Affairs Minister Partha Chatterjee told mediapersons here.
Chatterjee appealed to the Left Front and Congress legislators to back the resolution.
The minister said he has already spoken to Leader of the Opposition Abdul Mannan and would also discuss the matter with Left Front legislative party leader Sujon Chakraborty.
Chief Minister Banerjee said a day back that her government will pass a resolution against the Citizenship (Amendment) Act within three to four days.
Banerjee and her Trinamool Congress have been at the forefront of the widespread protests against the legislation in the state, which also saw violence and vandalism after the law was passed last month.
The Left and the Congress, which have also hit the streets against the Act, ridiculed the Trinamool several times over the past few days for not bringing any resolution against the CAA.
The Congress and Left had earlier in the month tried to bring such a resolution in the Assembly but the Trinamool did not agree, and the matter was not included in the list of business of the House.
However, on Tuesday Chatterjee claimed that he had submitted such a resolution to the Speaker ahead of the Left and the Congress, but the matter could not be raised as the House sat for a day's special session to pass the SC and ST Commission Bill on January 9.
"Who is in the forefront and who is not you have seen many a time. But the biggest victory is the one where people are at the forefront. And that will be a win-win situation. No democratic movement without the support of the people is possible in a win-lose situation," he said.
The CPI(M)-led Left Democratic Front (LDF) government in Kerala and Congress-ruled Punjab have already passed resolutions in the respective Assemblies demanding scrapping of the controversial CAA.
The CAA, passed in Parliament last month, seeks to provide Indian nationality to Hindus, Christ, Sikhs, Parsis, Jains and Buddhists who fled religious persecution in Pakistan, Afghanistan and Bangladesh till December 31, 2014.
As per the Act, such communities will not be treated as illegal immigrants now and will be given Indian citizenship.
( With inputs from IANS )