The Bolts tendered Turner at a first and third-round compensation level, but league sources have indicated that he can be had for less - but how much less is the question.
Turner will also visit the Buffalo Bills and they are also believed to be highly interested in his services.
Things had been quiet on the Turner front until this week - and three teams have shown interest with the Green Bay Packers reportedly backing out of the process.
Turner rushed for 502 yards last season in a backup role and has shown to be an explosive force when running the ball. He has averaged 6.0 yards per carry over his three-year career and had seven rushes of 20-yards or more last season.