Sosa has not made a decision regarding the contract offer from Washington, which is a non-guaranteed, one-year pact for $500,000.
"Sammy doesn't think of himself as someone who has to beg for a spot on a big league roster," said the source.
Washington's offer is the only one the Dominican slugger and potential Hall of Famer has received this winter.
With 588 career home runs, Sosa is the all-time leader among Latin American players. He had three years of 60 or more home runs between 1998 and 2001 as a Cub, becoming enormously popular in Chicago and throughout baseball.
However, injuries and some bad publicity, including the discovery of a corked bat in 2003, have affected his legacy and market value.
"Sammy wants to get to 600 home runs, but he's not willing to humiliate himself to keep playing. He feels that the lack of interest in his services this winter constitutes a humiliation," added the source.
Although the team has not set a deadline for a decision by Sosa, the Nationals would like to have the situation resolved before pitchers and catchers report to spring training on February 18. Washington originally only offered a minor league contract, with an invitation to spring training.
Sosa is taking his time to mull the decision, consulting with family and friends. Some have encouraged him to continue playing, while others have suggested he leave baseball.
Sosa, 37, was released by the Orioles after a disappointing 2005, when he hit .221 with 14 home runs and 45 RBI in 102 games.
The "Caribbean Bambino" was affected by various injuries last year, when he made $17 millon in the last season of a five-year deal he signed with Chicago in 2002. Baltimore declined a $18 million option for 2006.
The Nationals see Sosa as an insurance policy entering spring training, in case Jose Guillen's shoulder does not heal as quickly as they would like, and also with Alfonso Soriano's apparent refusal to switch from the infield to the outfield.