The deadline for tagging players is Monday at 4 p.m. ET.
Davis is the Colts' most physical corner, and at just 25 years old, he's entering the prime of his career.
Davis is ranked No. 15 overall on Around The League's top 101 free-agent list. However, he is the fourth-rated free-agent cornerback, behind Alterraun Verner, Aqib Talib and Brent Grimes. The depth at the position in free agency should give the Colts some leverage in working out a deal before Davis hits the open market.
The tag for cornerbacks sits at $11.834 million, which is high -- even for a player of Davis' caliber and importance in Indy's defense.
The Colts have plenty of salary cap space and would like to retain him -- just not at the franchise tag number.