Dreams dictionary: Press
Dreams dictionary: Interpretation 1
To see the press in your dream suggests that there is a messages that you need to convey and get across to others. You need to pay more attention to the outside world and not be so self-absorbed. Alternatively, the dream may be a pun on some "pressing" issue that needs your immediate attention.
Dreams dictionary: Interpretation 2
To dream that the press is chasing you indicates your lack of privacy. You may feel that someone or some situation is invading into your space.