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.