The group told councillors that unless an objection over the environmental suitability of the site is lifted within the next week, it could take the 100m project elsewhere, possibly to Belgium.
The news comes in the week that Polestar won a huge 5-year contract to print 8.7m Associated Newspaper supplements each week from Quebecor.
"This is a technicality and we've been categorically assured that it will be resolved very quickly," said Polestar project manager Mike Young. "Clearly we don't want our customers to be alarmed that we haven't got planning permission."
It emerged last week that a property developer who owns the site adjacent to Polestar's had raised an objection which legally forced the Government Office for Yorkshire and Humberside to issue a stop notice, blocking the granting of full planning permission.
But sources close to the project have suggested that the threat to pull out of Sheffield could be a way to force the Government Office's hand on the lifting of the stop notice.
One source said that Polestar "needed to give them [the local Government Office] a reason to make a decision by putting as much commercial pressure on them as possible".
Last Monday (21 June), planning permission was unanimously granted by Sheffield Council for the Tinsley site, pending the resolution of the stop notice, which had been served the previous Friday.
Construction on the site, adjacent to the M1, is due to start at the end of the first week of July. Young said that "ink on paper on the first press" was scheduled for the last week of March 2005, and that recruitment advertising would be appearing in the local press in the next week.
As PrintWeek went to press, Sheffield City Council and the Government Office for Yorkshire and Humberside were unavailable for comment.
Story by Josh Brooks