Daw made a sensational start to his AFL career against the Brisbane Lions last Sunday, kicking the game's opening goal inside the first minute after soaring over Lion Niall McKeever to take a strong mark.
But just 19 minutes later he was helped from the ground after an accidential head clash with teammate Ben Cunnington and was subsequently substituted from the game.
Saunders told AFL.com.au on Monday Daw had recovered well in the first 24 hours after the collision.
"Majak is being very closely monitored by the club doctor and has presented well throughout testing," Saunders said.
"We're really pleased with how he's recovered so far, but he'll be continually monitored during the week as he completes a heavily modified and gradually progressed training program."
Robbie Tarrant – whose leg injury paved the way for Daw to make his debut – is also well placed to play against the Hawks.
Tarrant carried a sore leg through North's opening three rounds of the season, but was ruled out of the Lions clash when he could not complete the Roos' main training session last Thursday.
"He's responded well to a week off as expected, and we expect him to present really well later in the week," Saunders said of Tarrant.
Nick Bowen covers North Melbourne news for AFL.com.au. Follow him on Twitter: @AFL_Nick