The 42-year-old also gave the Denver Nuggets a good chance of landing James.
"He's gonna look at Denver," Boykins added. "...The Nuggets have the young pieces that LeBron wants around him. They do.
According to Boykins, the key will be Denver keeping Nikola Jokic on a long-term deal. The center fits well as a big man who can shoot, dribble and pass, but he'll be an unrestricted free agent in 2019 if the Nuggets don't turn down his team option for this upcoming season.
Locking him up would greatly help the Nuggets' chances of landing James, according to Boykins.
"If they sign Jokic, it goes up to 35-40 percent," he said about the odds of signing the four-time MVP.
Boykins spent 13 seasons in the NBA with 10 different organizations, but his longest stretch came in Denver, where he played 255 games across four seasons.
Meanwhile, James is expected to hit free agency this season if he declines his $35.6 million player option for 2018-19.
According to OddsShark, the Los Angeles Lakers are the favorites to sign him, while neither the Knicks nor the Nuggets are listed among the top nine options.
Former Nuggets teammate Kenyon Martin said he believes James and Paul George will end up with the Knicks, but it seems as though Boykins has an inside source that says otherwise.