"It is part of the ongoing review that was launched in November, and it includes options to sell parts of the business," said the source.
The sale could result in as many as 10,000 job cuts, according to a report on the FT's website on Wednesday.
RBS and Lazard declined to comment on the situation.
RBS, 83 percent owned by Britain after a government bailout during the 2008 credit crisis, had already announced last year cutbacks to its investment banking division and plans to axe more jobs at the unit.
It came under further pressure to rein in the business, known within RBS as "GBM" (Global Banking & Markets), in December when British Finance Minister George Osborne told RBS to make "further significant reductions".
The Scottish bank's GBM unit is strong globally in bond trading, foreign exchange and American mortgage financing.