The east African country is expected to eventually compete with Australia and Qatar as a major provider of liquefied natural gas (LNG) to Asia.
Last year, Thai state oil company PTT Exploration and Production PCL trumped Royal Dutch Shell Plc in a hotly contested battle for Cove Energy Plc and its 8.5% of the field.
The $1.9 billion price tag for Cove implies the stake now on offer could fetch about $4.5 billion.
Dhoot, who controls consumer electronics to mobile-phone services conglomerate Videocon Group, is leading the process and has hired Standard Chartered and UBS to handle the sale, the sources added.
Both banks declined to comment. First round bids are due on March 14, one of the sources said.