Bourne is free to negotiate with other teams with the 49ers having the right to match any competing offer. Should it fail to do so, San Francisco will receive a second-round pick for the receiver.
This news comes after the report that San Francisco offered the same level tender to running back Matt Breida. The team also opted not to tender linebacker Elijah Lee.
Bourne, 24, is entering his fourth NFL season.
The 49ers signed Bourne as an undrafted free agent out of Eastern Washington in 2017. He registered 30 receptions for 358 yards with five touchdowns through 16 games in 2019. His best statistical season came in 2018 when he led the team's wide receivers with 42 catches for 487 yards with four touchdowns.
Bourne has 88 catches for 1,102 yards with nine touchdowns through his three NFL seasons.