Banerjee would be leaving for Delhi on Tuesday. The tentative time for Wednesday's meeting is 4.30 p.m.
The meeting will come at a time when the central probe agency CBI is involved in a legal battle for grilling the state's Additional Director General, CID, Rajeev Kumar, in connection with its probe into the Saradha ponzi scam.
Kumar, the Chief Minister's 'blue-eyed officer', had headed the Special Investigation Team formed by the Banerjee government in 2013 after the scandal running into billions of rupees came into the limelight when the Saradha group's companies shut shops one after the other duping thousands of people - particularly those from the economically weaker sections - who had parked huge amounts lured by the group's promise of astronomical returns.
The CBI has alleged that the SIT tampered with evidence in the case and also did not hand over important documents seized by it to the agency which took up the investigation following a Supreme Court order in 2014.
Banerjee's office sought an appointment on behalf of the Chief Minister with Modi to discuss the various demands concerning the state.
The Chief Minister is likely to raise the issue of the Central government allegedly curtailing the allocations for the state on development projects, and the progress of Centre-state joint welfare schemes. Besides, the situation after the publication of the final NRC list in Assam, issue of infiltration, and the Central and state governments' development projects in the Maoist belt could also figure in the discussions.
Banerjee would also interact with a number of leaders from various parties during her stay in the national capital.
She is likely to return either on Thursday or Friday.
This will be Banerjee's first meeting with the Prime Minister after the BJP came up with an impressive show in the April-May Lok Sabha polls in West Bengal bagging its best ever tally of 18 seats. The Trinamool, which had bagged 34 seats in the 2014 general elections, saw its number come down to 22. The two leaders had last met during the convention of the Visva-Bharati University last year.
Intensifying her opposition to the BJP, Banerjee had on multiple occasions during the past few months declined to visit Delhi to participate in meetings called by the centre.
( With inputs from IANS )