Allegations of harassment by a faculty member and reporting?
As Allure points out, opinions on this matter will vary, so let me note some points that I think are important here, and also offer an opinion that is slightly to the contrary of some other answers.  (For brevity, these points are framed as an answer to the person you are talking about who is the academic dealing with these students.)


Academics have a duty of care to students: Students at university are adults, but they mostly are still young and inexperienced.  In my humble opinion, academics should generally err on the side of pushing for assistance in cases like these, even if the students are reluctant.  Students are generally young adults who may be intimidated by the positions and standing of older adults who have attained academic success and institutional power.  Having another academic push the matter forward may be helpful in overcoming this disparity.
Harassers thrive on the "I won't make a fuss" mentality: Without making any assumption about whether or not harassment has actually occurred in this case, it is worth noting that cases of harassment tend to be done over and over again by a small number of individuals, and tend to proliferate because each person who is being harassed thinks it is only them, and they don't want to make a fuss and risk retribution by a powerful person.  In cases where a victim of harassment reports the conduct, it is not unusual for this to precipitate an avalanche of other allegations against the same harasser.  Recent events in Hollywood (e.g., Harvey Weinstein) testify to this fact, as do many other cases of sexual harassment.
Merely referring an allegation is not "accusatory": Reporting an allegation for it to be investigated need not presume the truth of the allegation, and need not be "accusatory".  That is the point of an investigation - to get to the truth from a starting point of it being unknown.  It is perfectly legitimate to report allegations you have heard on to the administration, while taking no position on whether they are true or false, but still asking the university to consider whatever investigation into the matter is warranted by the allegations.  There is no contradiction between wanting to bring this matter to the attention of the administration, and also wanting to avoid a false accusation.  Just make sure that if you do send an email to the administration, you write it in a neutral way that does not presume that misconduct has occurred.
In the end, evidence will be required: While it is legitimate to report hearsay allegations for the purpose of bringing a matter to the attention of the administration, you should bear in mind that your hearsay is not evidence.  Unless one of the affected students is willing to speak to the university administration about this, the university will probably be very limited in its ability to investigate the matter.  That is perfectly legitimate - after all, people should not be subject to negative proceeding against them without evidence, and hearsay evidence is weak evidence.
With this in mind, the contribution you can make here is to bring the allegation to the attention of the administration, leading to contact with the students, and giving them an opportunity to report this matter formally.  By acting as the initial referrer of the allegation, you can also show your students that actions are louder than words - you are willing to get involves, so maybe that will make them more willing.  Still, at the end of the day it will depend on them.  In my view even this step might be a good idea, even if the students ultimately decide not to proceed.  I don't agree with the recommendation to do nothing.
Have the courage to put your name to the referral: Think carefully about whether it is appropriate to report this anonymously.  If it is justifiable to refer the matter to the university administration, and if you frame your email in a fair way that does not presume misconduct, then you ought to have the courage to put your name to it, and stand by your own actions.  Reports of harassment are generally treated in confidence (at least up to the point where the accused is able to face the accusations), and this is an opportunity to set an example for your students and show that you are willing to act on your own principles.  If a grown-up academic can't show the backbone to make a report about a colleague, without hiding behind anonymity, why should younger students show the courage that is absent in their elders?


Anyway, that is my two-cents.  I'm sure there will be plenty of others with contrary opinions.  Hopefully others will also give their views, as it would be worth getting some contrary ideas on this matter before making your decision.