Ajayi is coming off a torn ACL suffered in October, so the team will likely do a thorough physical evaluation before potentially making an offer. It was the second time he tore an ACL after first suffering the injury at Boise State.
The issue caused him to drop to the fifth round of the 2015 draft despite obvious talent.
Prior to the injury, the 25-year-old had 183 rushing yards and three touchdowns in four games with the Philadelphia Eagles.
Despite the mediocre production even when healthy, Ajayi has proved himself in the past.
The Boise State product earned a Pro Bowl selection in 2016 with the Miami Dolphins when he rushed for 1,272 yards with eight touchdowns, and then he was a key part of the Eagles' Super Bowl run in 2017 while splitting time with LeGarrette Blount.
At 6'0", 223 pounds, he is a powerful runner between the tackles who has averaged 4.5 yards per carry in his career.
Even with young running backs like Marlon Mack and Nyheim Hines on the Colts roster, adding a bigger back like Ajayi could be useful in early downs and short-yardage situations. He could also help keep these players fresh, especially with Mack dealing with injury issues in his career.
The Colts will enter next season with high expectations after going 10-6 last year, so finding value on the free-agent market at any position could help the team reach its goals.