McIntosh has bid 185p a share for the pub company, City A.M. revealed today.
Heineken has made an approach of 174p a share for the company.
Punch Taverns issued a statement saying:
The board confirms that it has received a proposal from Patron Capital Advisers regarding a possible cash offer for Punch at 174 pence per Punch share. The Patron proposal is conditional on, amongst other things, the recommendation of the board. The board is in advanced discussions with Patron and Heineken regarding the Patron proposal.
The Board also confirms that it has also received an approach from Emerald Investment Partners Limited regarding a possible cash offer for Punch at 185 pence per Punch share.
The Emerald Proposal is conditional on, amongst other things, arranging committed financing, confirmatory due diligence, and the recommendation of the board.
Punch was formed in 1997 and now has a nationwide portfolio of around 3,300 pubs, making it one of the UK's biggest pub companies.
Shares were up more than 32 per cent to 170.25p in lunchtime trading.
Heineken is the Dutch brewing giant behind Strongbow and Foster's.
Any tie-up between Heineken, which already owns 1,100 leased pubs through its Star Pubs & Bars division, and Punch, which owns about 3,300 sites across the country, would be expected to face close scrutiny from competition regulators.
Punch last month reported its first annual profit since 2013, and said that it had reached the conclusion of a disposal programme aimed at reducing its huge debt pile.
Its improvement in its financial performance under new chief executive Duncan Garrood comes after years of complex restructuring which included a demerger of Spirit, the managed pubs company which was later bought by Greene King.