The share price values the struggling service at $5.3 billion, The New York Times reported.
"The buzz is huge. There hasn't been a privatization of that magnitude in a long while, and people think they can make an instant gain," said stockbroker David Scott at Redmayne Bentley.
"We've been absolutely inundated with calls from clients," Scott said.
The government said it would retain a 38 percent stake in the company, which dates back to the 16th century and the court of Henry VIII.
The government, however, could reduce its shares to 30 percent, allowing for sale of what is called an over allotment that comes into play if demand warrants it.
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