Wall Street firm Goldman Sachs Group Inc. in September quietly approached Citigroup Inc. about the possibility of merging the two firms' operations, according to a person familiar with the matter.

The call, placed by Goldman Chief Executive Lloyd Blankfein to counterpart Vikram Pandit at Citigroup, was made not long after Lehman Brothers Holdings Inc. filed for bankruptcy protection on Sept. 15, a move that sent the shares of rival brokers like Goldman and Morgan Stanley down sharply.

However,...