The state government had earlier said it would not encourage any SEZ in the West Bengal.
After meeting top brass of Infosys, Industry and IT Minister Partha Chatterjee said the company officials are willing to work closely with the state government.
"They told us that the company would be thinking on alternative lines for coming to the state for the first time and also showed confidence in the working of the government," he said.
The minister said he met Infosys Executive Co-Chairman S Gopalakrishnan and Senior VP Vinod Hampapur to discuss their proposed facility at Rajarhat.
"We do not want to pressurise them to come fast.
Let them take their time," he said, adding that the company would join hands with the state in approaching the Centre for allowing fiscal benefits outside special economic zone bracket.
According to Chatterjee, Infosys officials said that since operating in an SEZ entails huge fiscal benefits from the Centre, it would be unviable for them to forgo the status.
As per the SEZ Act, units and developers enjoy huge tax benefits including income tax holidays for 10 years.
Meanwhile, Infosys said in a statement that it discussed the issues around the proposed Infosys Development Center in Kolkata with the minister.
"We have agreed to work together towards finding a solution," the company said. Recently, Infosys had also written to the state government seeking possession of land at Rajarhat near here.
The state had earlier allotted 50 acre of land to the state for Rs 75 crore (Rs 750 million).