Murphy, 27, has been participating in the Dogs' recent heat chamber training in preparation for the Top End's climate, despite being a late withdrawal from Friday night's side against Richmond.
The Dogs are optimistic Murphy will be available to play at TIO Stadium after taking that extra week off.
"He'll have a test later in the week," football operations manager James Fantasia said on Monday night.
"The withdrawal was because there was still a bit of uncomfortableness, and rather than risk anything, we just felt it was maybe better to be cautious and wait rather than rush it.
"We'll consider taking him to Darwin. He's been in all the training, and it was just precautionary why we held off on him on Friday."
There is an alternative plan for Murphy that doesn't involve the long flight north, with the Dogs considering playing him in Williamstown’s VFL match against Geelong at Burbank Oval on Saturday.
Fantasia said Murphy’s replacement, Brennan Stack, had done enough in his debut game to put a case forward for a second senior appearance this weekend.
"It's nice when you're able to bring a player up and keep him there. That's always the preference," he said.
"In saying that, we've still got to pick a side this week that can beat Port Adelaide, who are coming off a good win ... [Stack’s] done enough to keep his spot; it's just a matter of who he's up against."
The Bulldogs will take 23 players to Darwin on Thursday, with Lindsay Gilbee still nursing a bruised ankle and Murphy an uncertain starter.
Fantasia said the Dogs' link with Darwin, which extends back to their first game in the city in 2004, meant the club was confident in their preparation and routine when playing in the warm climate.
He also said older players would not be rested from the long trip.
"That's not going to be a factor. We're confident the guys have been getting through recovery and we've been training a little bit with heat chamber work," he said.
"We'll go up on Thursday and train up there that day, because we find that comfortable.
"Our routine has worked pretty well so we won't change anything."
Scott Welsh is available for selection after serving a one-match suspension, while rookie-listed ruckman James Mulligan will miss a few weeks after hurting his quad in the VFL on the weekend.
