Goldman Sachs declined to comment, while no one at Citi was immediately available for comment.
Blankfein's call was made shortly after Goldman got the approval to become a commercial bank on September 21 and with the knowledge of regulators, the source said.
With Morgan Stanley, Goldman is one of only two large investment banks that have survived independently, though the two have subjected themselves to closer regulatory scrutiny in return for access to central bank funding.
The Financial Times reported the call first on its website on Sunday. The conversation between the two bankers was brief as Pandit turned down the proposal immediately, the paper said, citing unnamed sources. The FT added that a deal would have been structured as a Citi takeover of Goldman.