The 49ers reportedly considered a deal for Beckham last offseason and remain interested heading into 2019.
Though the receiver missed the final four games of the season due to injury, he still finished the year with 77 catches for 1,052 yards and six touchdowns.
The 26-year-old has three Pro Bowl selections in his five-year career and was twice named second-team All-Pro.
Despite his success on the field, the Giants remain open to a trade.
Seth Wickersham of ESPN The Magazine reported the team was "50-50" on possibly moving Beckham last offseason, while they were seeking two first-round picks in return. There was also chatter about a midseason deal before the deadline.
Although Beckham signed a five-year extension in the offseason, he can still be traded while clearing $16.75 million off the books, per Florio. The move would also cost the Giants a cap charge of $16 million.
If the Giants pull the trigger, it makes sense for the 49ers to be there waiting.
San Francisco is in need of an offensive playmaker who can take advantage in head coach Kyle Shanahan's offense. Tight end George Kittle set a new NFL record at his position with 1,377 receiving yards this year, but none of the receivers topped 500 yards.