The potential transfer or creation of roles by the US bank in France was first reported by French newspaper Les Echos, without giving a timeline for when they might be completed.
Morgan Stanley already employs around 120 bankers in Paris, and Reuters reported last July the bank has chosen Frankfurt to be its main base for its EU operations after Brexit.
Its move to transfer some staff there follows a similar pattern to other banks which have picked one EU centre to be their main regional subsidiary in the bloc, but then locating other parts of their businesses in several countries.
Swiss bank UBS earlier this month said it would pursue a decentralised approach, with staff mainly moving to Frankfurt and other locations where their clients are based.
US and European banks are starting to execute contingency plans, after British Prime Minister Theresa May ruled out retaining passporting rights for financial services.