The Owls had the one-time Brentford and Chelsea midfielder on trial at Hillsborough but will not be proceeding further.
The 26-year-old, a free agent having been released by Brentford at the end of last season, was invited by former manager Steve Bruce to join Wednesday's pre-season training camp in Portugal earlier this month.
McEachran, who came through the ranks at Chelsea, was given run-outs in Wednesday's friendlies at Lincoln City and Northampton Town, and despite Bruce parting company with the club, the player continued to train with the Owls.
The midfielder was among the squad that travelled to Germany, and played in their two warm-up fixtures against VFB Lubeck and Holstein Kiel, but on Wednesday, Bullen announced that the two parties had parted company.
"I spoke to Josh the other day and I told him that with our managerial situation that it was better for him to look at other avenues with regards to going on trial elsewhere," Bullen told The Star.
McEachran, who was believed to be on the radar of Aston Villa earlier this summer, was on Chelsea's books from 2001 to 2015 but only made a handful of first-team appearances, going on to get numerous loan stints under his belt.
After leaving Stamford Bridge permanently, the £1.35million-rated player (Transfermarkt) joined Brentford in 2015 and spent four years playing for the Griffin Park outfit.
Have something to tell us about this article?