Naiyaravoro is seen by many as a replacement for Scotland winger Sean Maitland, who left the Warriors over the summer to join London Irish.
And now that Naiyaravoro, who spent last season playing for the New South Wales Waratahs, will not be required for the Rugby World Cup, Townsend is keen to get him up to speed as soon as possible.
"We are still waiting for the visa process to be started," Townsend told The Scotsman.
"He's now back in Australia after being out in the States with the Australia squad but he's come back early to speed up the visa process now he is no longer with the Australia squad.
"These things can take two or three weeks. I'm hoping for less. We have a game in three weeks against Munster and it would be great news if we could have him for that.
"Then the next game is a fortnight after so if not Munster then we'd like to think he'd be here for that one."
One signing that the GUINNESS PRO12 defending champions already have available is forwards coach Dan McFarland, who will be able to share some secrets about his former club, Connacht, when they visit Scotstoun tonight.
"He certainly brings good insight, he was there 17 years," added Townsend.
"Who knows what they will do this week knowing that Dan is now here as a coach. We'll expect an excellent set-piece.
"They were ranked the best scrum last season, second best at scoring tries from driving mauls, very effective in contact and, on top of that, you've got a coach in Pat Lam who wants the team to play and move the ball."
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