It is thought the bids, which are understood to be from rival property companies, could lead to an auction for the group.
Analysts are believed to have valued the company's shares at about 350p each, potentially valuing the company at '560m. In early trading the shares soared 27 per cent, or 64.25p, to 314p.
Reports said the London-based group's financial advisers, Lehman Brothers and HSBC, are likely to handle the auction, which could trigger interest from larger rivals such as Hammerson, British Land and Land Securities.
The group's portfolio includes about '800m of investment property in the capital, and it has planning permission for a massive new retail centre in Croydon.
Minerva, which also owns department store chain Allders, is currently developing the tallest building in the Square Mile.
The Minerva Tower, in St Botolph Street, would be 712ft tall and provide one million square foot of office space, as well as shops, over 50 floors.
In March the group pre-tax profits from its core rental activities fell to '600,000, from '1.2m the previous year.
Overall, it made a '4.4m loss against a '1.19m profit a year ago due to losses at Allders.
No one from Minerva was available to comment. Tweet

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