A letter from the French company to Unite, which contained assurances that De La Rue's UK production sites would not be affected in the event of a takeover, was leaked to The Observer this weekend.
Unite assistant general secretary Tony Burke confirmed that it would not meet Oberthur until after it made a bid for De La Rue, which it has not yet done.
He said: "Our members at De La Rue are highly skilled, and we are worried that any takeover will follow in the footsteps of Kraft's takeover of Cadbury last year when it closed a British factory.
"News that the letter from Oberthur has been sent to a national newspapers was unhelpful. No one at Unite gave them the letter, and we don't know who did."
He added that as it is now public, the letter has also been published to Unite's members.
Burke said: "The proper way to deal with any speculation over how UK staff will be treated following any bid for a UK company is for Unite to advise our representatives.
"This is the normal procedure in a case like this, and a meeting will be held towards the end of month."
There has also been speculation that Oberthur is looking into finding finance to acquire De La Rue through a private equity group, although Burke said that this is news to him.
He said: "If this speculation is the case, it is very unwelcome as they will not necessarily be interested in the print industry and may just be after a quick return."
The London Stock Exchange Takeover Panel has given Oberthur a deadline of 5pm on 7 February to make clear its intentions over De La Rue.
Oberthur declined to comment.