Source: Sharecast
Bakkavor was considering the enhanced proposal, newswire Bloomberg reported, citing unnamed sources.
Two takeover bids from Greencore were rejected by Bakkavor this month, with the latest cash-and-stock offer valued at 189p a share valuing the target at £1.14bn.
Greencore shareholders would own approximately 59.8% and Bakkavor shareholders would own approximately 40.2% of the enlarged group.
"The enlarged group would create a leading UK convenience food business with a combined revenue of ca £4bn, with a diverse product offering, strong commercial relationships and market-leading capabilities in attractive segments across the UK convenience food landscape," Greencore said in a statement on March 14.
Dublin-based Greencore supplies food including sandwiches, chilled prepared meals and cooking sauces to supermarkets in the UK as well as travel retail outlets and coffee shops.
Bakkavor's customers include Tesco, Mark & Spencer and Sainsbury's and also operates in the US and China.
Reporting by Frank Prenesti for Sharecast.com