"Probably either on February 20 or 21, the meeting is proposed," a top state government official said.
"The state government has sent a request to the Union government for clearance," he said.
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Powell's wish to meet Banerjee ahead of the Lok Sabha polls due in May has led to speculation.
She had met Banerjee, the Trinamool Congress chief, in September 2012 and discussed possible US investments among other matters.
In May the same year, the then US Secretary of State Hillary Clinton had met Banerjee.
Ending a nine-year boycott, the US Ambassador had yesterday met Modi at Gandhinagar and said her country looked forward to working closely with the government India chose after the Lok Sabha elections.