Action, short of a strike, was initially scheduled to begin on Saturday (19 September), after Trinity announced a nationwide pay freeze last year.
However, all sites except for Oldham have agreed terms and no industrial action has begun anywhere.
Negotiations at Oldham are expected to conclude this week, although Unite national officer Steve Sibbald said that action could still take place at the Greater Manchester facility.
He added: "This was always more about assurances regarding individual bargaining and each site now has that assurance. We have also had discussions regarding a possible bonus, which we were not expecting. If that does happen Trinity will probably be doing better than most in its sector."
Any bonus would still be dependent upon targets being met, Trinity has said.
Although Unite may see the assurance as a victory, Trinity has maintained that individual bargaining was something that would always be maintained outside of "extraordinary" trading situations.
A Trinity Mirror spokesman said: "We are pleased that the majority of members have agreed not to pursue industrial action.
"Throughout this process all we have done is confirm what has always been our position on local bargaining and on a potential bonus in 2009, and we can now concentrate our efforts on steering the business through some of the most challenging trading conditions the industry has ever faced."