The Times has listed four possible candidates for the British and Irish Lions job – Hansen, Warren Gatland, Eddie Jones and Joe Schmidt.
The appointment is expected to be made before the World Cup with the selected candidate starting in January 2020.
While it can't be ruled out, any Hansen announcement before the World Cup is very unlikely.
When Hansen announced last December he was stepping down at the end of this season, he said he had no plans post World Cup, where the All Blacks will look to win three straight.
"I haven't thought about what I will do after the World Cup. It is such a great privilege to coach the All Blacks and I am focused on nothing more than the next 21 months as we have an incredible opportunity to do something that no other team has ever done before," he said.
Gatland has coached the Lions on the previous two tours, a series win in Australia followed by the 1-1 series in New Zealand. The Kiwi stands down as Wales coach following the Rugby World Cup as does Irish coach Schmidt.
Both have been named as possible candidates for the Lions job however Schmidt plans to return to New Zealand, stating he plans to give up coaching for good, while Gatland has been linked to the England job to replace Jones.