There is no certainty that Medivation will agree to a sale with any party, the people cautioned.
The sources asked not to be identified because the deliberations are confidential. Medivation and Sanofi declined to comment, while Pfizer and Celgene did not immediately respond to requests for comment.
Medivation shares jumped as much as 4.2 percent on the news and were trading up 2.5 percent at $61.62 in afternoon trading in New York.
Sanofi's new offer, whose terms could not be immediately learned, came following conversations with Medivation shareholders. Last month, shareholder advisory firm Glass Lewis & Co recommended that Medivation's shareholders should not support Sanofi's efforts to replace the company's board members.
Sanofi wants Medivation - which sells a successful prostate cancer drug called Xtandi - so Sanofi can expand in the lucrative oncology sector, as it seeks new businesses to compensate for flagging diabetes revenues.
Reuters had reported in May that Medivation had signed confidentiality agreements with some companies, including Pfizer.
Medivation had previously argued that Sanofi's offer had failed to value fairly the prospects for Xtandi, as well as two other products currently in clinical trials - Talazoparib, for the treatment of breast cancer, and Pidilizumab, for the treatment of blood cancers.