The two leaders will come together in the state for the first time since the Lok Sabha polls in May.
"As far as we know, she (Banerjee) will attend a programme of the Kolkata Port Trust (KoPT) on January 12, where the prime minister would also be present," a senior Trinamool Congress leader told PTI.
Sources said there could also be a meeting between the PM and the chief minister at the Raj Bhawan, though nothing has been finalised in this regard as yet.
Mansukh Mandaviya, the Minister of State for Shipping had personally gone to the state secretariat on Friday to invite Banerjee to the 150th anniversary programme of KoPT on Sunday.
Modi will be on a two-day visit to the city from January 11.
Banerjee had on Thursday said in the state assembly that she would boycott an opposition meeting called by Congress interim president Sonia Gandhi on January 13 over the JNU violence, the Citizenship Amendment Act and other "antipeople" policies of the Centre.
Ever since the BJP emerged the main contender of the TMC in West Bengal following the Lok Sabha poll results, Modi and Banerjee have not shared the dais at any government programme.
The chief minister had gone to New Delhi in September last year and met Modi in a "courtesy call" visit.
The new citizenship law has emerged as the latest flashpoint in the state, with the TMC opposing the contentious legislation tooth and nail, and the BJP pressing for its implementation.
Meanwhile, reacting to the likely meeting of the two leaders, the opposition CPI(M)-led Left Front said the Trinamool Congress' "double standard" is now exposed.
"The TMC is actually a Trojan horse in the opposition camp," CPI(M) legislative party leader Sujan Chakraborty alleged.
The West Bengal BJP leadership, however, said it is expected that in a federal structure, a chief minister will be present at a government programme attended by the prime minister.