Activities that would need to move equate to about 20% of revenue earned by HSBC's investment bank division in London.
Speaking from the World Economic Forum in the Swiss ski resort Davos, Gulliver said in an interview that "about 1,000 jobs which are carrying out activities which are covered by European legislation... would probably need, in our case, to go to France".
While Gulliver had in the past already hinted at such a switch of investment banking jobs, his comments appeared more precise as he suggested France would take precedence over other EU nations.
"We bought Credit Commercial de France in 2002, so we have a full service universal bank in France. And so for us, it's France."
Activities covered by European financial regulation that would need to move equate to about 20 percent of revenue earned by HSBC's investment bank division in London, Gulliver added.
He was speaking Tuesday, shortly after British Prime Minister Theresa May said Britain would pull out of the European single market to control EU immigration, as she unveiled plans for a clean break from Brussels for the first time.
At the same time however, May stressed the need for the greatest possible access to the market with Britain as an outsider.
The UK financial sector has long feared the loss of "passporting" rights -- which allows EU member states to trade across national borders. That provides a crucial gateway for companies to access the rest of the bloc.
Lobby group the British Bankers' Association cautioned in October that international lenders with operations in the UK are ready to transfer some of their activities out of the country from early 2017.