The leading global bank, which has assets worth $2.6 trillion (£1.9 trillion), has said it will relocate the jobs if the UK leaves the single market, a possible outcome of post-Brexit negotiations, according to the BBC.
It is possible the UK could leave the EU but remain a part of the European Economic Area (EEA), in a model similar to that of Norway, Iceland and Liechtenstein.
Employees at HSBC in Canary Wharf, who already process payments made in euros, would join the 10,000 currently based in the French capital under the plans.
A number of other large financial companies including Morgan Stanley, BNP Paribas and JPMorgan have reportedly also made plans to reduce the size of their businesses in the UK, following the referendum result on Thursday.
HSBC currently employs around 48,000 people in the UK, and around 260,000 across the world.
HSBC, which carries out a significant amount of its business in Asia, considered moving its headquarters to Hong Kong earlier this year.
But the company decided to remain in London in part due to the city's status as the main financial centre of Europe.
Douglas Flint, HSBC's chairman, said on Friday: "The work to establish fresh terms of trade with our European and global partners will be complex and time consuming.
"We will be working tirelessly in the coming weeks and months to help our customers adjust to and prepare for the new environment."
François Villeroy de Galhau, governor of the Bank of France, said this week: "It would be a bit paradoxical to leave the EU and apply all EU rules, but that is the solution if Britain wants to keep access to the single market.
Brexit reactions – in pictures
Brexit reactions – in pictures
Supporters of the Stronger In campaign look at their phones after hearing results in the EU referendum at London's Royal Festival Hall
Leave supporters cheer results at a Leave.eu party after polling stations closed in the Referendum on the European Union in London
Mr Cameron announces his resignation to supporters
Donald Tusk proposes that the 27 remaining EU member states ‘start a wider reflection on the future of our union’
Ukip leader Nigel Farage greets his supporters on College Green in Westminster, after Britain voted to leave the European Union
Supporters of the Stronger In Campaign react as referendum results are announced today
Boris Johnson leaves his home today to discover a crowd of waiting journalists and police officers
Leave EU supporters celebrate as they watch the British EU Referendum results being televised at Millbank Tower in London
Supporters of the Stronger In Campaign react as results of the EU referendum are announced at the Royal Festival Hall
Supporters of the Stronger In campaign react after hearing results in the EU referendum at London's Royal Festival Hall
"The City cannot keep this European passport and clearing houses cannot be located in London either."
HSBC forecast this week that inflation could increase to 4 per cent within 18 months after the pound sterling’s Brexit-induced collapse.
HSBC declined to comment.