The tour to Australia will be the Glasgow head coach's first chance to work with his full squad after he takes over from Vern Cotter.
Speaking to the Scottish Rugby website, Gregor said: "It's a case of timing. I feel hugely privileged to be given the Scotland job and our first opportunity to work with the players is at the same time as the Lions tour.
"I was approached a couple of weeks ago - and I was obviously flattered - but my priority now is Glasgow and at the end of the season Scotland are going on tour, so that's the priority then.
"I had a good think and didn't give an immediate answer. I really wanted to reflect on what was involved but I quickly realised that the Scotland tour to Australia is my number one priority at the end of this season.
"At international level you don't get that much access with the players. This is the most access you'll get with them. On a tour you get to work with them, preparing them and spending time with them, so that's the biggest factor."