Lord Sugar, who was made Baron Sugar of Clapton in July 2010, served as a government enterprise "tsar" under Gordon Brown.
Adding further criticism, the Jewish businessman reposted a message from Conservative pundit Guido Fawkes that said: "Ken has claimed that he has no idea how much his wife earns. He is the director of the company that pays her."
However Lord Sugar did not offer himself up as an alternative. "It's been suggested I run for mayor," he wrote. "Not possible, too many commercial conflicts, no time, more to the point I would not know where to start."
