The person spoke on condition of anonymity Monday because no deal had been announced.
The 33-year-old Affeldt went 1-2 with a 2.70 ERA in 67 appearances spanning 63 1-3 innings this season for the World Series champions.
When the season ended, Affeldt said he wanted to stay with San Francisco but needed a multiyear deal to give some security for his family - he has a wife and three young sons. Affeldt also was a key member of the bullpen during the club's 2010 run to the franchise's first championship since 1954.
General manager Brian Sabean called re-signing Affeldt one of his top offseason priorities.