The two things are not mutually exclusive. A motion for injunctive relief would require that he had filed suit. That being said, there is no way any court would order injunctive relief, unless (and this would never happen) the Times reporters admitted that they knew the information was false at the time they wrote their stories.
Obviously I don't expect a lawsuit to actually be brought, though with Trump one never knows. In practice such a suit would open Pandora's box to all of the evidence regarding Trump's other acts of harassment and/or evidence of his admitting to engaging in conduct of this nature (since truth is a defense to defamation, and the fact that he has engaged in other unwelcome contact and bragged about it is at least potentially probative on the question of whether the allegations the Times posted are true). This could even, potentially, lead to a successful subpoena of all of the raw footage from the Apprentice. Even if no discovery were conducted, I find it hard to understand how the Times could successfully be sued for defamation, since they apparently interviewed not only the accusers but other people the accusers had told about his conduct shortly after it happened (not to mention the fact that Trump is on record bragging about having engaged in precisely the kind of conduct these women claim occurred). If Trump were foolish enough to sue the Times (he is, after all, an exceptionally foolish man), the ensuing release of damaging information would make what we've seen so far look like what it probably is - the tip of the iceberg.