The newspaper quoted unnamed investors who said they understood a move was "more than likely" and that there had been a "change of tone" as HSBC <0005.HK> reviews its domicile, something the bank does every three years.
A spokesman for the bank played down the story, saying:
"No decision whatsoever has been made.
A British tax on bank assets to be introduced this year would cost HSBC about $600 million based on its balance sheet at the end of December. That marks a cost for being based in the country, HSBC said last week as it cut its profitability targets alongside its 2010 results.
Political rhetoric in the UK has become more aggressive toward the banks, as public anger at the cost of the taxpayer bailout of lenders RBS <RBS.L> and Lloyds <LLOY.L> and the paying of generous bankers' bonuses has risen.
Bankers hit back after Bank of England Governor Mervyn King gave an outspoken interview in Saturday's Telegraph, in which he said the banking industry needed urgent reform and that there was a risk of a fresh crisis.
But finance minister George Osborne defended King, saying to Sky News on Sunday: "I wouldn't be (putting King in charge of bank regulation) if I didn't broadly agree with his concerns and I'm also very particularly looking at the issue which he correctly raises which is how do we deal with the "too important to fail" problem."
The system of regulation had completely failed, Osborne said.
The Sunday Telegraph also said that the publication of a report into RBS's collapse in 2008 by the regulator, the Financial Services Authority, was likely to be delayed from March to at least April.
(Reporting by Rosalba O'Brien and Keith Weir; Editing by Jon Loades-Carter)