His Glasgow side begin their European Champions Cup campaign against Sale on Saturday, but the deadline for applications for the All Blacks coaching job is Monday.
He hasn't applied yet for the New Zealand role but admitted to BBC Scotland that he was still thinking about applying but wasn't prepared to elaborate on that.
"We've spent the last six months trying to get a bit of clarity around our future and we're getting pretty close to making that decision," Rennie said.
"It'll be clearer in the next couple of weeks."
Rennie said he tended to keep away from all the speculation around the position. It was a high-profile job with a lot of interest in who would succeed Steve Hansen, and there were a lot of high-quality candidates.
Whatever happens Rennie will have to see out his Glasgow season and that is why the Champions Cup is so important to him.
"The quality of this competition is phenomenal. Europe is clearly the toughest club competition in the world, tougher than Super Rugby," he said.
The weekend game with Sale was a 'must-win', Rennie said.
It's his third attempt to take Glasgow further in the competition. They reached the quarterfinals last year but went down 27-56 to Saracens, on the back of some frustrating scrum decisions made by referee Nigel Owens.
Sale are fourth in the Premiership but are down on star power for the game which will be played in Scotland.
World Cup winner halfback Faf de Klerk is not yet back with the side and neither are Tom Curry and Mark Wilson, both members of the beaten England team. Springbok lock Lood de Jager is still suffering from the shoulder injury he had at the World Cup.
However, Glasgow go into the game without international fullback Stuart Hogg who has joined Exeter. Last season they lost Finn Russell.
"It's the way it is here," Rennie said.
"Your best players are probably going to be targeted by bigger clubs. When you talk about trying to replace people like Finn and Hoggy with the same sort of quality, it costs a hell of a lot of money."
Younger players were coming through and it was a case of doing what happened with Russell and Hogg, giving them a chance from a young age.
"Other guys will fill their shoes, but it might just take a couple of years," he said.