According to Armando Salguero of the Miami Herald, the Dolphins are hoping to make a pitch to Stills this week, but sources believe he is more likely to test the free-agent waters.
Per Salguero, Stills is expected to command around $12 million per season on the open market, a price Miami is unwilling to pay.
The 24-year-old Stills is coming off arguably his best season, as he reeled in 42 receptions for 726 yards and a career-high nine touchdowns.
Miami acquired him from the New Orleans Saints prior to the 2015 season, and while Stills' first campaign with the Dolphins was a struggle to the tune of just 440 yards and three touchdowns, he became a key part of the offense in 2016.
Stills is a good fit in Miami since he is among the NFL's most dangerous deep threats, which allows Pro Bowl receiver Jarvis Landry to do damage underneath defenses.
The 2013 fifth-round pick out of Oklahoma was only third on the team in receiving yardage last season, though, behind both Landry and DeVante Parker.
If Parker continues to make strides and Miami manages to find a cheaper deep option either through the draft or free agency, it may be able to let Stills walk without experiencing too much of a drop-off.