In February the company announced plans to leave its Harmsworth Quays print facility and move out of London to a greenfield site in Thurrock.
However, sources close the company have said that the board will meet early next month to decide whether to go ahead with the move or follow the Daily Telegraph down the contract print route.
A spokesman for DMGT said that the company would not comment on speculation, but added: "DMGT is in discussion with staff and continues to evaluate its options."
At this stage it is rumoured that the newspaper will follow the Telegraph to News International's print subsidiary Newsprinters.
News International did not wish to comment, but a spokeswoman for the publisher said: "We are a contract printer; we print the Telegraph and the Financial Times as well as some regional titles."
According to the union, DMGT has yet to enter into an official consultation with employees about the closure of Harmsworth Quays.
National officer Steve Sibbald said he would be surprised if the title is moved to Newsprinter's Broxbourne facility.
He said: "As I understand it they would not be able to get in because there are no slots available. We understood that they were moving a lot more copies to the Didcot plant."
If the title did move to Newsprinters, it would be moving away from flexo printing and would likely have to change its size, in line with the current format of The Sun.