Q:

Is it OK for a reference to contact the hiring manager first? 

I've recently been asked to be a reference for a previous colleague.  The hiring manager of the said colleague mentioned that he will be reaching out to my colleague's referees shortly. 
Its been a 3-4 business working days and I have not heard from the hiring manager.  This colleague of mine has been an exemplary worker and I would really like to provide a good reference for him. 
Is it OK for a reference to contact the hiring manager first and set up a call?  

A:

Its been a 3-4 business working days

Some hiring departments work a lot slower than this. 

Some employers may just pretend to obtain references, but not actually bother. 

Some employers may just pick one or two references from a list, and if they do they're likely to pick superiors (and ignore colleagues on the same level.) 

Is it OK for a reference to contact the hiring manager first and set up a call? 

If I had this sort of a call, I'd be a bit suspicious and if anything it could work against the candidate or at least result in your reference being discarded.  It sounds a bit like, as his friend, you think he'll get bad references elsewhere, so you want to definitely make sure a good one goes on record. 
Also remember that references are really nothing more than a pass/fail tick-box exercise.  If bad references are given, then that certainly works against the candidate - but there's really little to no difference between a "standard" and "exemplary" reference in most scenarios - they'll both result in the candidate getting the job. 
Just let things run their natural course, and make sure you give a good reference if asked. 

A:

Is it OK for a reference to contact the hiring manager first and set up a call?  

No, this is just not done.  Convention says that hiring managers reach out to references on their own time, if at all.  If you tried this you would effectively be trying to interfere with the company's hiring process which will probably reflect poorly on you and by extension the candidate.  
Now while usually the hiring manager simply calls up a reference when that's convenient, it is normal for a candidate to give a heads-up in cases where reaching someone might be difficult.  If for instance a reference is in a time zone half a world away then it would be better for the hiring manager and the reference to arrange a phone call via email.  But that's not what you're asking about.  Effectively forcing your reference on the hiring manager is just not a good look.