According to TMZ Sports, no teams have reached out to Kaepernick even though several franchises are having issues under center in terms of performance and injuries.
Allen—Buffalo's rookie starter—has missed the past two games with an elbow injury, and there is no definitive timetable for his return.
Kaepernick has not played since starting 11 games for the San Francisco 49ers in 2016.
Although he went 1-10, he threw for 2,241 yards, 16 touchdowns and four interceptions while rushing for 468 yards and two scores.
Kaepernick also has six games of playoff experience, and he led the Niners to Super Bowl XLVII.
The 30-year-old has filed a collusion lawsuit against the NFL due to his belief that he remains unsigned because of his decision to kneel during the playing of the national anthem in 2016 to protest social injustice and racial inequality.
When asked Wednesday about whether the Bills considered signing Kaepernick, head coach Sean McDermott revealed little, per WGRZ: "Yeah, I know [general manager] Brandon [Beane] is always looking at the different options available to us. So, we'll leave it at that."
Rather than signing Kaepernick, Buffalo went with the 28-year-old Barkley and his 11 games of NFL experience.
Barkley made six starts for the Bears two seasons ago, going 1-5. The former USC standout also threw for 1,611 yards, eight touchdowns and 14 interceptions that season.
All told, Barkley has eight passing touchdowns and 18 interceptions on 266 career pass attempts.
Peterman, who has three touchdown passes and nine interceptions on 81 career attempts, is expected to start when Buffalo faces the Bears on Sunday.