France's Sanofi-Aventis has agreed to raise its bid for Genzyme Corp to the low $70's per share range, plus a milestone payment based on the performance of an experimental drug, a source familiar with the situation said.

The total valuation for Genzyme depends on the outcome of due diligence as Sanofi looks at the U.S. biotech company's financial records, one source said on Tuesday.

Sanofi agreed to raise the takeover price from its initial offer of $69 per share in order to gain access to Genzyme's books, that source said. Still, Sanofi did not raise the offer as high as the $75 per share value Genzyme had sought, that source said.

The final valuation could be in the very high $70's, including the contingent value right (CVR), or payout over time based on the performance of Genzyme's experimental multiple sclerosis drug, Lemtrada, a second source said.

Bloomberg reported the total value would be in the range of $76 or $77 per share, including the potential future payout.

Citing people with knowledge of the talks between the two companies, the Bloomberg report said Sanofi may increase its initial $69 per share offer by $2 per share in cash.

It would also add a CVR of up to $6 per share if Genzyme's Lemtrada drug for multiple sclerosis proves successful, according to the report.

Genzyme could not be immediately reached for comment. Sanofi declined to comment.

On Monday, Reuters reported that the two companies had hammered out an agreement in principle on deal terms, pending due diligence.

A deal could be reached in the next week or so, ahead of a February 15 deadline for Sanofi's tender offer to shareholders, a source previously told Reuters.

Genzyme has repeatedly rejected Sanofi's $18.5 billion, or $69 per share, hostile offer launched in early October. The two sides have been slowly moving closer in direct talks in recent weeks.

The two companies have been discussing a potential deal, including a CVR for several weeks, trying to bridge a wide gap in their expectations for Lemtrada. Genzyme has forecast peak annual sales of $3.5 billion, while Sanofi, using the average of several analyst estimates, expects only about $700 million.

A CVR is a tradable instrument whose value will depend on how much investors believe in the prospects for Lemtrada.

Shares in Genzyme fell 1 percent to $72.59 on Tuesday as investors were expecting a higher upfront cash payout.

(Reporting by Michele Gershberg, Toni Clarke and Jessica Hall; Editing by Tim Dobbyn, Phil Berlowitz)