Warren Gatland's freak accident means the Kiwi coach will not take charge of the side Down Under, with Rob Howley taking the reins, and Warburton has revealed an imminent trip to the specialist will decide his fate.
The openside flanker damaged nerves in his shoulder during Wales' Six Nations-clinching 16-9 win over France and said: "I still hope to go to Australia, of course, I do.
"I'm going to London next week to see a specialist. Hopefully he will give me the all clear and it will be just a few more weeks before I can return.
"Nerves are a funny thing so it's hard to be specific at this moment in time, but my fingers are crossed.
"Although I'm gutted I'm not playing for the Blues, every cloud has a silver lining and I'm able to nurse other injuries.
"I did really want to get back for the Blues and I believed I owed them a bit for being away with the national squad.
"It's unfortunate timing really and I won't be able to play for the rest of the season.
"I could come back and cause further damage, so it's better to remain out until the end of the season."