Some 300 staff are employed across the two sites, although St Ives said only "a small number" of its Leeds employees would be affected.
The decision is based on the group’s strategy to provide higher value-added printing and marketing services and further reduce dependence on sheetfed print.
St Ives chief executive Patrick Martell said: "Bradford is a very big site with spare space, and by consolidating the two operations we can be more efficient."
As part of the restructure, the Bradford facility will be refurbished to improve the layout and workflow and to house some mailing kit brought over from Leeds, which St Ives described as being "in a poor state of repair".
St Ives Direct managing director Jim McKie confirmed that a "small number" of jobs are at risk but said that the group is aiming to keep redundancies to a minimum by transferring staff across from Leeds.
"We will look at ways to keep the number of compulsory redundancies to a minimum," he said.
Full consultation on the proposals will take place in the next few weeks.
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