The Giants had made signing Lincecum and Matt Cain to long-term contracts a high priority this offseason. Lincecum's current contract expires after the 2013 season, and Cain's ends after the 2012 season.
CBSSports.com reported that the Giants apparently raised an earlier offer to Lincecum that was for four years and about $80 million, but Lincecum is looking for an eight-year deal.
The two sides are also considering a one-year or two-year deal if they can't agree on a long-term deal.
A long-term deal for Lincecum probably would cost the Giants more than $100 million, according to CBSSports.com, but they want to avoid arbitration as well. Lincecum made $14 million in 2011, and he could make around $20 million in an arbitration settlement for 2012 and perhaps $25 million or more in 2013.