Reddy's visit to Kolkata is part of his nationwide tour to garner support for a united Andhra Pradesh.
Trinamool Congress chief is also battling the demand for a Gorkhaland state in the northern parts of West Bengal.
The meeting also assumes importance in view of the 2014 general elections
The meeting also assumes importance in view of the 2014 general elections, with many observers feeling that the regional parties could play an important role in government formation at the centre.
The outcome of the meeting was yet unknown.
Banerjee has already urged the regional parties to come together.
The YSR Congress president, facing charges in assets cases, is out on bail. A special CBI court in Hyderabad Tuesday gave him the go ahead to visit Kolkata.
Reddy, who has already met BJP president Rajnath Singh, Communist Party of India Marxist (CPI-M) and Communist Party of India (CPI) leaders, is expected to meet Samajwadi Party leaders including Uttar Pradesh Chief Minister Akhilesh Yadav Thursday.