This is according to a senior government source who told Reuters on Monday.
The east African nation, which is rated B+ by Standard and Poors, launched its Eurobond roadshow this month.
The government source, who declined to be named, would not give further details about the marketing campaign.
Analysts said the issue was attracting high demand because it comes in two tenors with a five-year tranche offering investors a minimum 6 percent return and a 10-year portion guaranteeing a yield of 7 percent.
"I am not too surprised (by the demand) given the wider product offering," said a fixed-income trader in Nairobi.
"Investors have a different appetite for debt depending on the duration and once the Eurobond market develops, you might find multi-tenor offers become more popular to cater for refinancing risk," the added.
Traders said the pricing of the Kenyan five-year offer was cheaper than the existing Senegalese one of the same tenor, while the 10-year tranche as cheaper than the one issued by Zambia earlier this year.
The Kenyan government has said proceeds of the Kenyan bond will be used to repay an existing syndicated $600 million loan and finance infrastructure projects.