Minerva, whose main developments are the Walbrook and St. Botolphs office blocks in the City of London, said it received a possible cash offer of 120.5p a share, from a consortium of investors.
The developer's shares jumped as much as 16pc and were up 13pc to 112.25p in lunchtime trading.
The consortium -made up of funds advised by Area Property Partners and a subsidiary of DV4, which was advised by Delancey Real Estate Asset Management - is bidding through a special purpose vehicle called Jupiter Properties.
The 120.5p-a-share price is a 21.4pc premium to Minerva's closing share price of 99.25p yesterday, and a 53.5pc premium to its share price on January 13 of 78.5p.
Minerva shareholders last year rejected moves by Nathan Kirsh, the South African investor who had built up a 29.5pc stake in the company, to oust management.