Though the 36-year-old Rodgers has four years remaining on his contract with the Packers, Green Bay's decision to draft Love signaled uncertainty at the quarterback position in the coming seasons.
"Oh, man," Rodgers said with a laugh. "That's a tough thought right there."
The Bears have their own quarterback uncertainty. Mitchell Trubisky, the No. 2 overall pick in 2017, is entering the final year of his rookie contract and is set for a position battle against veteran Nick Foles as training camp opens.
The Bears declined Trubisky's fifth-year option for 2021, leaving Foles as their only quarterback under contract beyond this 2020 season.
Rodgers has played his entire 15-year NFL career with the Packers.