Babalj continued his trial with the Roar on Monday, training with the team as they prepare for Friday's home clash with Western Sydney Wanderers.
The 27-year-old has been on the lookout for a new club after leaving Indian Super League team Atletico de Kolkata in November.
An 18-year-old A-League debutant who played twice for Australia in 2012, Babalj has struggled to find form across several clubs after rupturing an anterior cruciate ligament against Brisbane at Suncorp Stadium in early 2016.
The Roar are on the hunt for an experienced striker following Adam Taggart's recent departure to South Korean powerhouse Suwon Bluewings last month.
Babalj has been trialling over the past week along with Victorian National Premier League left-back Jacob Alexander.
Interim coach Darren Davies said both players had impressed but there were no plans as yet to offer either a deal.
"We've had a number of players away as well with the Olyroos, so we're a little bit low on numbers and they obviously added to the numbers but they've been great," Davies said.
"They've worked hard and we'll see where we go.
"(It's) constantly a work in progress but nothing confirmed as yet."
One player who has signed on with the Roar is teenaged fullback Izaack Powell.
The 17-year-old schoolboy, who became the Roar's youngest A-League player when he debuted off the bench in the 2-1 win over Sydney FC last month, has signed a scholarship contract for the 2019-20 campaign.
Roar defender Jack Hingert (knee) and midfielder Stefan Mauk (groin) are also beginning their rehab programs after successfully undergoing surgery on their season-ending injuries in the past two weeks.
