Crew took the veteran striker in the second round of December's Re-Entry Draft but the club and player have yet to see eye-to-eye about a second stint for the prolific goalscorer at Columbus Crew Stadium.
Cunningham spent seven seasons with the Crew between 1998 and 2004, scoring more than 60 league goals along the way, but Bliss has revealed the 34-year olds mooted return has not gone as planned.
MLS combine two weeks ago)," Bliss said.
"Unless the guy's willing to play for the offer that was out there 12 to 13 days ago, then we're not any closer."
Cunningham left the US to trial with Norwegian club IK Start but a report over the weekend stated that he would not be joining the Tippeligaen outfit.
Crew coach Robert Warzycha was remaining hopeful that the club could still secure the services of the MLS' second all-time leading scorer.
"It is very, very, close," Warzycha said of a deal. "We are staying where we were before. We offered him a contract, and he just has to agree to it because we negotiated for some time and we came up with some number and obviously that's what it is going to be. It is up to him to grab it."