The newspaper said the auction comes as Nigeria prepares to impose harsher terms on foreign operators and hand greater control to domestic firms.
The oil giant, which declined to comment on the report, is the biggest and longest standing Western oil producer in Nigeria.
But production has been hampered by insecurity in the oil-rich Niger Delta, government funding shortfalls and an uncertain regulatory environment.
The report coincided with a group led by Shell pledging on Sunday to spend tens of billions of dollars developing Iraq's Majnoon supergiant oilfield over the next two decades.
The Sunday Times said it understood Shell recently launched a formal sales process overseen by Ann Pickard, head of Shell Nigeria.
Chinese state-owned oil group Sinopec had requested information, it said, and Nigeria's independent oil group Oando and London-listed Afren could also be interested.
In Beijing, Sinopec was not immediately available for comment while domestic peer CNOOC -- reported in September as being in talks with Nigeria to buy large stakes in some of Africa's richest oil blocks -- declined to comment.
Shell has switched investment from Nigeria, which supplied 16 percent of its 2008 oil production, in response to growing violence from militants and a souring of relations with the government.
(Reporting by Paul Sandle; editing by John Stonestreet)