The Bears put the transition tag on Fuller earlier this month with a one-year salary of $12.9 million. That gives the Bears the right to match any offer Fuller gets, and the Bears have five days to make that decision.
The amount of money in the offer sheet Fuller signed with the Packers remains unclear.
When the Bears placed the transition tag on Fuller, general manager Ryan Pace said the team was buying time to reach a long-term deal with Fuller.
If the Bears do not match the offer, they will lose Fuller and receive no compensation in return from the Packers.
Fuller has been a starter in all three of his seasons with the Bears and has eight career interceptions. That includes two picks he made while starting all 16 games in 2017.