Miller, who is a free agent, put advanced talks about joining the Denver Nuggets on hold to explore the option after learning James was going to Cleveland, sources said.
Miller and James have a close relationship and played together for three seasons with the Miami Heat. Miller won two title rings alongside James before the Heat released him via the amnesty provision last summer.
After dealing with thumb, shoulder and back injuries and needing five surgeries in his first three years in Miami, Miller was healthy and played in all 82 games this past season for the Memphis Grizzlies. He averaged 7.1 points and shot 46 percent from 3-point range.
Late Friday, Miller announced on his Instagram account he will not return to the Grizzlies next season.
"Just informed the Grizz are going in another direction," he wrote. "I completely understand, but wanted to thank you so much for everything. Awesome city. Awesome fans. Thank you for the opportunity. I will always love Memphis #letitfly."
The Cavs would have their $2.7 million "room exception" they could offer Miller. In addition, Miller is being paid $6.6 million next season by the Heat to finish out the five-year deal he signed in 2010.