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Hansen revealed last week that he would make a decision about his future – whether to stick with the All Blacks beyond 2019 or pass the baton – at the end of this year.
Robertson – who is off-contract with the Crusaders after the 2019 Super Rugby season – said he will be keeping a close eye on developments.
"You look at everything every time this thing comes up," Robertson said on Tuesday.
"When you are a coach, you have to look at all the options – that's what I'm doing at the moment.
"The All Black job doesn't come up that often does it? When it does, you have to have a really good look at it.
"The decision from Steve [Hansen] will play a really big part of it."
Ireland head coach Joe Schmidt – who many tipped to be the man to replace Hansen – announced late on Monday night (NZT) that he will "finish coaching" after the World Cup in Japan to "prioritise family commitments".
Schmidt's shock decision leaves the door open for the likes of Robertson should Hansen decide to step away.