Francisco, who is owed $6.5 million during the upcoming season, underwent surgery in December to remove a bone spur from his right elbow.
But Alderson said Francisco is having a routine recovery from the relatively minor elbow procedure that is not expected to impact him during spring training. Instead, Francisco's underwhelming performance last season has the Mets considering other options.
Francisco, 33, went 1-3 with a 5.53 ERA in 48 relief appearances in 2012. He recorded 23 saves in 26 chances.
"I think a lot will depend on what we see over the course of February and into March," Alderson said. "I think that's something that will be determined in the course of spring training. Health is an issue. Performance is an issue."
Alderson said the Mets' offseason bullpen renovation is done, with the exception of completing a deal with right-hander Brandon Lyon. As a result, right-hander Bobby Parnell would appear the primary alternative to Francisco, with the yet-to-be-officially-signed Lyon as the secondary alternative.
Parnell produced a 0.60 ERA and .191 batting average in 15 appearances in September as Francisco dealt with an elbow issue. He converted all three save chances that month.
The Mets recently pursued free agent Jose Valverde, the former closer of the Detroit Tigers, major league sources told ESPNNewYork.com. But Alderson made it clear Monday that the bullpen overhaul, which included the additions of Scott Atchison, LaTroy Hawkins and Pedro Feliciano on minor league deals, is complete after a resolution with Lyon.