Hero Enterprise Investment Office and the Burman Family Office had made a binding offer to invest Rs 8 billion through a preferential share issue at Rs 167 apiece and Rs 10 billion via preferential issue of warrants at Rs 176 per warrant.
The recommendation by Fortis' board would be sent to shareholders for approval, Fortis said.
Hero Enterprise is an investment company formed by Sunil Munjal, a member of the family that runs India's largest motorcycle maker Hero. The Burman Family Office is the private investment arm of the family that owns consumer goods company Dabur India.
The keen interest in Fortis, which runs some 30 hospitals in India, comes as investors look to tap soaring demand for private healthcare in the country against the backdrop of a stretched public healthcare system.
Private hospitals could also be boosted from Prime Minister Narendra Modi's plans to implement a healthcare programme aimed at providing insurance cover to about half of India's population.