Brian O'Driscoll has revealed he intends to stay on as Ireland captain but at 32 he is entering the twilight of his international career, and Muller believes 29-year-old Best has all the attributes needed to fill the void.
"Rory would be a brilliant Ireland captain," said Muller, who has guided Ulster to ninth in the RaboDirect PRO12 table.
"He can compete with anyone on the world stage, which is brilliant not only for Irish rugby but also for Ulster rugby - he is a world-class player."
"Having played under him at Ulster, I know he has got great leadership qualities and knows when to take the tough decisions.
"He has got great character as well, which is probably the first thing I look for in a leadership role, and I have no doubt if he becomes the next Irish captain that he will do a smashing, smashing job.
"I've followed Rory for quite a bit now, both with Ulster and watching him with Ireland, and I've never seen him play this kind of rugby he's playing now. He's in the form of his life and was outstanding at the World Cup."
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