It is currently considering leaving its Harmsworth Quays base and relocating to a 20-acre greenfield site in Thurrock, Essex.
A spokesman for DMGT said that "a good number" of the facility's 157 employees would be offered the chance to move to Thurrock.
It appears the move will be followed by an investment in printing capabilities. However, the company said new machines were not on the radar.
A statement from DMGT said that the move would make it more efficient to "upgrade existing flexo presses and reconfigure them more efficiently".
The spokesman said: "It is early days, so plans are far from definite. But the site has an outdated press layout that costs higher than most to run. Moving would mean the company would avoid spending on an aged building. Thurrock would also offer excellent distribution."
Under the plan, the presses will move over a period of three to four years, with both sites running parallel until completion. At that point, the London site would close, although DMGT said it intended to keep the facility.
It is anticipated that, if the plans go ahead, the building will be completed in 12 months' time.
DMGT said the move would cost around £45m-£50m, but added that it would have cost around £30m-£35m to upgrade its presses and building at Harmsworth Quays.
Its Thameside location is attractive to developers so the company would likely be able to recoup a far greater figure through property development.
The Daily Mail publisher has four locations across the UK. As well as its London facility it has an £80m flagship site at Didcot, which opened in 2008, as well as sites in Stoke and Derby.
Unite national officer Steve Sibbald said: "What we want of course is for as much redeployment as possible. It is the same for all of these new facilities, although moving to Thurrock is not as dramatic as going from the Isle of Dogs to Luton.
"There is an inevitability about these moves; it is like a second wave since Wapping. We have to accept the inevitability of it and hope that there is an industry here still in 25 years' time."
