Verjee, best known for bringing the Domino's Pizzas franchise to Britain, has donated 77,000 pounds to the Liberal Democrats since May 2010.
According to 'The Sunday Times', he is now being lined up as one of the next batch of Lib Dem Lords.
The Uganda-born businessman, who also owns the posh crystal and silverware shop Thomas Goode in Mayfair here, is believed to have a number of offshore business interests.
Lib Dem leader Clegg and other party ministers have sharply criticised business people who operate offshore.
However, according to senior party sources quoted by the newspaper, Verjee is now being actively considered for the list of Lib Dem peers to be submitted to 10 Downing Street.
Any peerage for Verjee is likely to cite his charitable activities in India, East Africa and the UK. He received a CBE for his support for the arts and alleviation of HIV/AIDS in Africa 2009.
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Brompton Capital, the company he used to donate to the Lib Dems, was until last month owned by Integro Nominees (Jersey) Limited, based in the Channel Island tax haven.
However, the shares were transferred to Rumi Verjee and Khaled Verjee last month.
Company documents show the shares are held by Lawgra Limited, which in turn is owned by Breezy Holdings, based in another tax haven