Citing people with knowledge of the talks between the two companies, the report said Sanofi may increase its initial $69 per share offer, or $18.5 billion, by $2 per share in cash.
It would also add a contingent value right payment of up to $6 per share if Genzyme's Lemtrada drug for multiple sclerosis proves successful, according to the report.
Sanofi and Genzyme officials were not immediately available to comment on the report.
On Monday, Reuters reported that the two companies had hammered out an agreement in principle on deal terms, pending due diligence.
Shares in Genzyme fell 1.2 percent to $72.47 as investors were expecting a higher upfront cash payout.
(Reporting by Michele Gershberg)