"The coverage could exceed 67% and go up to 70%," an official said, requesting anonymity.
Gandhi is also understood to have asked the government to ensure that existing levels food allocations should be maintained.
Although the bill itself will only guarantee monthly food handouts of 5kg for every entitled person, or 25 kg for a family of five - the average size of an Indian household - Gandhi has asked the government to continue current allocations, which is 35 kg in some states.
The existing allocations - higher than what is proposed under the food bill -- will be made operational through an "executive order", or an administrative decision.
Currently, 25 million households across the country receive 35 kg of food aid every month under the "Antyodaya Anna Yojana".
Gandhi is said to told the government that unless these vulnerable families are covered, a food security law would be meaningless.
The Planning Commission is finalizing a list of parameters that states need to adopt to decide who should be kept out of food handouts.