It is the latest in a stream of so-called "Swissleaks" allegations that have hit the reputation of the British banking giant and caused a political storm ahead of a general election in May.
The report claims the chief executive was a client of the Swiss private banking arm accused of helping wealthy clients evade tax. Gulliver held about USD 7.6 million in 2007 in a Swiss account in the name of Worcester Equities Inc, a Panama-registered company, according to the yesterday's report.
Gulliver, who is based in Britain but is domiciled in Hong Kong for legal and tax purposes, was listed as the beneficial owner of the account, the report said.
It was published on the evening before Gulliver is due to present HSBC's annual report, expected to be overshadowed by a scandal that has prompted investigations of the bank by Britain's financial watchdog and Swiss authorities.
HSBC did not immediately respond to a request for comment by AFP. However, a representative for Gulliver told the Guardian that the chief executive had used a Swiss account to hold his bonus payments prior to 2003, when he moved from Hong Kong to London.
Gulliver's lawyers said that Hong Kong tax had been paid on this income and that his Swiss accounts had been declared to British tax authorities. British newspapers published a letter from Gulliver apologising for the Swiss division's behaviour in full-page advertisements last week.
Gulliver insisted the Swiss arm had been "completely overhauled" since 2007, when former employee Herve Falciani stole a huge cache of data and passed it to French authorities.
British tax authority HM Revenue and Customs (HMRC) officials, accused of failing to act adequately on evidence of tax evasion in the files, are to be grilled by members of parliament on Wednesday.