The stock was 4.52 per cent higher at Rs 159.40 on the BSE.
The proposed open offer comes nine months after IHH walked out of bilateral negotiations with promoters Malvinder and Shivinder Singh, who were then in control.
The move is likely to set off competition with a TPG-Manipal Hospitals combine as each side tries to acquire a minimum holding of 51 per cent, going up to as much as 75 per cent stake in the company, ET reported.
The IHH's move to re-engage with Fortis follows failed negotiations with Global Health, the parent of Naresh Trehan-founded Medanta hospitals, for a potential deal valued at around Rs 5,800 crore, said sources tracking the developments.
Last June, IHH pulled out of exclusive negotiations on Fortis just days before signing on the dotted lines, worried about the legal implications of the battle between Daiichi Sankyo and the Singh brothers and unconvinced that it would gain undisputed ownership of the shares.